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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '550.16', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [20, 220, 20, 20], 'aut_gens': [[1, 110, 1210], [44621, 55000, 3630], [14241, 49280, 27830], [48161, 48730, 50820], [45751, 990, 21780]], 'aut_group': None, 'aut_hash': 5242072359972702651, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2662000, 'aut_permdeg': 715, 'aut_perms': 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'aut_phi_ratio': 110.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 1, 4, 1], [5, 121, 5, 4], [10, 121, 4, 1], [10, 121, 5, 4], [11, 10, 1, 1], [11, 11, 10, 1], [11, 110, 1, 1], [11, 110, 10, 1], [22, 121, 10, 1], [55, 10, 4, 1], [55, 11, 40, 1], [55, 110, 4, 1], [55, 110, 40, 1], [55, 121, 50, 4], [110, 121, 40, 1], [110, 121, 50, 4]], 'aut_supersolvable': True, 'aut_tex': '\\He_{11}.C_5^3.C_2^3.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '20.3', 'autcent_hash': 3, 'autcent_nilpotent': False, 'autcent_order': 20, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '133100.be', 'autcentquo_hash': 6501023867853927099, 'autcentquo_nilpotent': False, 'autcentquo_order': 133100, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': '\\He_{11}:C_{10}^2', 'cc_stats': [[1, 1, 1], [2, 121, 1], [5, 1, 4], [5, 121, 20], [10, 121, 24], [11, 10, 1], [11, 11, 10], [11, 110, 11], [22, 121, 10], [55, 10, 4], [55, 11, 40], [55, 110, 44], [55, 121, 200], [110, 121, 240]], 'center_label': '5.1', 'center_order': 5, 'central_product': True, 'central_quotient': '13310.bf', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '5.1', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 28, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['13310.bf', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 1, 4, 1], [5, 121, 4, 5], [10, 121, 4, 6], [11, 10, 1, 1], [11, 11, 10, 1], [11, 110, 1, 1], [11, 110, 10, 1], [22, 121, 10, 1], [55, 10, 4, 1], [55, 11, 40, 1], [55, 110, 4, 1], [55, 110, 40, 1], [55, 121, 40, 5], [110, 121, 40, 6]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 864, 'exponent': 110, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[110, 0, 4]], 'familial': False, 'frattini_label': '11.1', 'frattini_quotient': '6050.c', 'hash': 1745369678053108262, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [110, 11, 11], 'inner_gens': [[1, 24420, 55660], [43451, 110, 1210], [12101, 110, 1210]], 'inner_hash': 7716340785735456673, 'inner_nilpotent': False, 'inner_order': 13310, 'inner_split': True, 'inner_tex': 'C_{11}^2:C_{110}', 'inner_used': [1, 2], 'irrC_degree': 110, 'irrQ_degree': 440, 'irrQ_dim': 440, 'irrR_degree': None, 'irrep_stats': [[1, 550], [10, 55], [110, 5]], 'label': '66550.bb', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C5*C11^2:C110', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 30, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 610, 'number_divisions': 34, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 116, 'number_subgroups': 5712, 'old_label': None, 'order': 66550, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 121], [5, 2424], [10, 2904], [11, 1330], [22, 1210], [55, 29520], [110, 29040]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 20, 'outer_gen_orders': [20, 10], 'outer_gen_pows': [0, 0], 'outer_gens': [[13361, 6820, 45980], [39951, 49390, 55660]], 'outer_group': '200.45', 'outer_hash': 45, 'outer_nilpotent': False, 'outer_order': 200, 'outer_permdeg': 12, 'outer_perms': [4032871, 120516481], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{10}\\times F_5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 126, 'pgroup': 0, 'primary_abelian_invariants': [2, 5, 5, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 12], [10, 3], [40, 13], [100, 1], [110, 1], [400, 1], [440, 1]], 'representations': {'PC': {'code': '241644623303204829464473488976780342260187167488915039939', 'gens': [1, 4, 5], 'pres': [6, -2, -5, -11, -11, -5, -11, 12, 67, 586083, 368289, 130959, 1669804, 471910, 178, 435605, 435611]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 44917258509383164, 8899890620707361, 31989787875090175, 36687300164533435, 26379173019723849]}, 'Perm': {'d': 126, 'gens': [200464803256984606619883443733590402414244149409396229620917583308972449975215692363404199777395284220507115800144099745945825652435692673175295368314842368252958355902069898452928807164649218841398770504533166, 390286052597316776301165235354029453802711457695311114699484420628193014046590961100818202312786430183052841949032124367172522229233645320468785273368835270673770024190226788413368459426440117249673052101489263, 77, 579988317155910388073384916159803293943038328370163435963780115841490167624373801348420553767666047957284374090413314164805022974292719165755196228279460898037145542645156698978824254651422920613846776431797680, 16776440859409146353874654561279843963541076007232327513029236765259465847694610256514660171808976160226630531017989786321762933140727084049545647714657092393888556197093179208527286121703608710016853323159663, 771365699227586707103482607974451502297495655011087612286395721576689010719606469570932797533584490449322526778175807777182637085430901449657316018991939339896140733612182012582543415727806806331077134975716320]}}, 'schur_multiplier': [5], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5, 110], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times C_{11}^2:C_{110}', 'transitive_degree': 605, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 166466735
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 28, 'group_order': 66550, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 166466846
{'aut_label': '2A', 'centralizer': '121.a1.a1', 'counter': 2, 'group_counter': 28, 'group_order': 66550, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 55, 'size': 121}
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id: 166466957
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 28, 'group_order': 66550, 'label': '5A1', 'order': 5, 'powers': [5, 1, 3], 'representative': 13310, 'size': 1}
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id: 166467068
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 28, 'group_order': 66550, 'label': '5A-1', 'order': 5, 'powers': [6, 1, 4], 'representative': 53240, 'size': 1}
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id: 166467179
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 28, 'group_order': 66550, 'label': '5A2', 'order': 5, 'powers': [4, 1, 5], 'representative': 26620, 'size': 1}
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id: 166467290
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 28, 'group_order': 66550, 'label': '5A-2', 'order': 5, 'powers': [3, 1, 6], 'representative': 39930, 'size': 1}
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id: 166467312
{'aut_label': '5B1', 'centralizer': '121.a1.a1', 'counter': 7, 'group_counter': 28, 'group_order': 66550, 'label': '5B1', 'order': 5, 'powers': [9, 1, 7], 'representative': 22, 'size': 121}
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id: 166467323
{'aut_label': '5B-1', 'centralizer': '121.a1.a1', 'counter': 8, 'group_counter': 28, 'group_order': 66550, 'label': '5B-1', 'order': 5, 'powers': [10, 1, 8], 'representative': 88, 'size': 121}
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id: 166467334
{'aut_label': '5B2', 'centralizer': '121.a1.a1', 'counter': 9, 'group_counter': 28, 'group_order': 66550, 'label': '5B2', 'order': 5, 'powers': [8, 1, 9], 'representative': 44, 'size': 121}
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id: 166466736
{'aut_label': '5B-2', 'centralizer': '121.a1.a1', 'counter': 10, 'group_counter': 28, 'group_order': 66550, 'label': '5B-2', 'order': 5, 'powers': [7, 1, 10], 'representative': 66, 'size': 121}
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id: 166466747
{'aut_label': '5B1', 'centralizer': '121.a1.a1', 'counter': 11, 'group_counter': 28, 'group_order': 66550, 'label': '5C1', 'order': 5, 'powers': [13, 1, 11], 'representative': 56892, 'size': 121}
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id: 166466758
{'aut_label': '5B-1', 'centralizer': '121.a1.a1', 'counter': 12, 'group_counter': 28, 'group_order': 66550, 'label': '5C-1', 'order': 5, 'powers': [14, 1, 12], 'representative': 15818, 'size': 121}
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id: 166466769
{'aut_label': '5B2', 'centralizer': '121.a1.a1', 'counter': 13, 'group_counter': 28, 'group_order': 66550, 'label': '5C2', 'order': 5, 'powers': [12, 1, 13], 'representative': 4884, 'size': 121}
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id: 166466780
{'aut_label': '5B-2', 'centralizer': '121.a1.a1', 'counter': 14, 'group_counter': 28, 'group_order': 66550, 'label': '5C-2', 'order': 5, 'powers': [11, 1, 14], 'representative': 49676, 'size': 121}
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id: 166466791
{'aut_label': '5B1', 'centralizer': '121.a1.a1', 'counter': 15, 'group_counter': 28, 'group_order': 66550, 'label': '5D1', 'order': 5, 'powers': [17, 1, 15], 'representative': 47212, 'size': 121}
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id: 166466802
{'aut_label': '5B-1', 'centralizer': '121.a1.a1', 'counter': 16, 'group_counter': 28, 'group_order': 66550, 'label': '5D-1', 'order': 5, 'powers': [18, 1, 16], 'representative': 31548, 'size': 121}
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id: 166466813
{'aut_label': '5B2', 'centralizer': '121.a1.a1', 'counter': 17, 'group_counter': 28, 'group_order': 66550, 'label': '5D2', 'order': 5, 'powers': [16, 1, 17], 'representative': 9724, 'size': 121}
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id: 166466824
{'aut_label': '5B-2', 'centralizer': '121.a1.a1', 'counter': 18, 'group_counter': 28, 'group_order': 66550, 'label': '5D-2', 'order': 5, 'powers': [15, 1, 18], 'representative': 32736, 'size': 121}
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id: 166466835
{'aut_label': '5B1', 'centralizer': '121.a1.a1', 'counter': 19, 'group_counter': 28, 'group_order': 66550, 'label': '5E1', 'order': 5, 'powers': [21, 1, 19], 'representative': 37532, 'size': 121}
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id: 166466847
{'aut_label': '5B-1', 'centralizer': '121.a1.a1', 'counter': 20, 'group_counter': 28, 'group_order': 66550, 'label': '5E-1', 'order': 5, 'powers': [22, 1, 20], 'representative': 47278, 'size': 121}
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id: 166466858
{'aut_label': '5B2', 'centralizer': '121.a1.a1', 'counter': 21, 'group_counter': 28, 'group_order': 66550, 'label': '5E2', 'order': 5, 'powers': [20, 1, 21], 'representative': 14564, 'size': 121}
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id: 166466869
{'aut_label': '5B-2', 'centralizer': '121.a1.a1', 'counter': 22, 'group_counter': 28, 'group_order': 66550, 'label': '5E-2', 'order': 5, 'powers': [19, 1, 22], 'representative': 15796, 'size': 121}
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id: 166466880
{'aut_label': '5B1', 'centralizer': '121.a1.a1', 'counter': 23, 'group_counter': 28, 'group_order': 66550, 'label': '5F1', 'order': 5, 'powers': [25, 1, 23], 'representative': 27852, 'size': 121}
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id: 166466891
{'aut_label': '5B-1', 'centralizer': '121.a1.a1', 'counter': 24, 'group_counter': 28, 'group_order': 66550, 'label': '5F-1', 'order': 5, 'powers': [26, 1, 24], 'representative': 63008, 'size': 121}
-
id: 166466902
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id: 166466913
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id: 166466924
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id: 166466935
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id: 166466946
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id: 166466958
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id: 166466969
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id: 166466980
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id: 166466991
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id: 166467002
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id: 166467013
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id: 166467024
{'aut_label': '10A-1', 'centralizer': '121.a1.a1', 'counter': 36, 'group_counter': 28, 'group_order': 66550, 'label': '10C-1', 'order': 10, 'powers': [16, 2, 36], 'representative': 52129, 'size': 121}
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id: 166467035
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id: 166467046
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id: 166467057
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id: 166467069
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id: 166467080
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id: 166467091
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id: 166467102
{'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 43, 'group_counter': 28, 'group_order': 66550, 'label': '10E1', 'order': 10, 'powers': [23, 2, 43], 'representative': 4851, 'size': 121}
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id: 166467113
{'aut_label': '10A-1', 'centralizer': '121.a1.a1', 'counter': 44, 'group_counter': 28, 'group_order': 66550, 'label': '10E-1', 'order': 10, 'powers': [24, 2, 44], 'representative': 37609, 'size': 121}
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id: 166467124
{'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 45, 'group_counter': 28, 'group_order': 66550, 'label': '10E3', 'order': 10, 'powers': [26, 2, 45], 'representative': 20603, 'size': 121}
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id: 166467135
{'aut_label': '10A-3', 'centralizer': '121.a1.a1', 'counter': 46, 'group_counter': 28, 'group_order': 66550, 'label': '10E-3', 'order': 10, 'powers': [25, 2, 46], 'representative': 15807, 'size': 121}
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id: 166467146
{'aut_label': '10F1', 'centralizer': '121.a1.a1', 'counter': 47, 'group_counter': 28, 'group_order': 66550, 'label': '10F1', 'order': 10, 'powers': [5, 2, 47], 'representative': 1265, 'size': 121}
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id: 166467157
{'aut_label': '10F1', 'centralizer': '121.a1.a1', 'counter': 48, 'group_counter': 28, 'group_order': 66550, 'label': '10F-1', 'order': 10, 'powers': [6, 2, 48], 'representative': 41195, 'size': 121}
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id: 166467168
{'aut_label': '10F1', 'centralizer': '121.a1.a1', 'counter': 49, 'group_counter': 28, 'group_order': 66550, 'label': '10F3', 'order': 10, 'powers': [3, 2, 49], 'representative': 27885, 'size': 121}
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id: 166467180
{'aut_label': '10F1', 'centralizer': '121.a1.a1', 'counter': 50, 'group_counter': 28, 'group_order': 66550, 'label': '10F-3', 'order': 10, 'powers': [4, 2, 50], 'representative': 14575, 'size': 121}
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id: 166467191
{'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 51, 'group_counter': 28, 'group_order': 66550, 'label': '11A', 'order': 11, 'powers': [51, 51, 1], 'representative': 6050, 'size': 10}
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id: 166467202
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 52, 'group_counter': 28, 'group_order': 66550, 'label': '11B1', 'order': 11, 'powers': [54, 60, 1], 'representative': 10, 'size': 11}
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id: 166467213
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 53, 'group_counter': 28, 'group_order': 66550, 'label': '11B-1', 'order': 11, 'powers': [55, 61, 1], 'representative': 100, 'size': 11}
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id: 166467224
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 54, 'group_counter': 28, 'group_order': 66550, 'label': '11B2', 'order': 11, 'powers': [58, 53, 1], 'representative': 20, 'size': 11}
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id: 166467235
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 55, 'group_counter': 28, 'group_order': 66550, 'label': '11B-2', 'order': 11, 'powers': [59, 52, 1], 'representative': 90, 'size': 11}
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id: 166467246
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 56, 'group_counter': 28, 'group_order': 66550, 'label': '11B3', 'order': 11, 'powers': [61, 58, 1], 'representative': 30, 'size': 11}
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id: 166467257
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 57, 'group_counter': 28, 'group_order': 66550, 'label': '11B-3', 'order': 11, 'powers': [60, 59, 1], 'representative': 80, 'size': 11}
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id: 166467268
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 58, 'group_counter': 28, 'group_order': 66550, 'label': '11B4', 'order': 11, 'powers': [57, 55, 1], 'representative': 40, 'size': 11}
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id: 166467279
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 59, 'group_counter': 28, 'group_order': 66550, 'label': '11B-4', 'order': 11, 'powers': [56, 54, 1], 'representative': 70, 'size': 11}
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id: 166467291
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 60, 'group_counter': 28, 'group_order': 66550, 'label': '11B5', 'order': 11, 'powers': [53, 56, 1], 'representative': 50, 'size': 11}
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id: 166467302
{'aut_label': '11B1', 'centralizer': '11.b1.a1', 'counter': 61, 'group_counter': 28, 'group_order': 66550, 'label': '11B-5', 'order': 11, 'powers': [52, 57, 1], 'representative': 60, 'size': 11}
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id: 166467304
{'aut_label': '11C', 'centralizer': '110.b1.a1', 'counter': 62, 'group_counter': 28, 'group_order': 66550, 'label': '11C', 'order': 11, 'powers': [62, 62, 1], 'representative': 6600, 'size': 110}
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id: 166467305
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 63, 'group_counter': 28, 'group_order': 66550, 'label': '11D1', 'order': 11, 'powers': [65, 71, 1], 'representative': 18750, 'size': 110}
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id: 166467306
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 64, 'group_counter': 28, 'group_order': 66550, 'label': '11D-1', 'order': 11, 'powers': [66, 72, 1], 'representative': 12820, 'size': 110}
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id: 166467307
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 65, 'group_counter': 28, 'group_order': 66550, 'label': '11D2', 'order': 11, 'powers': [69, 64, 1], 'representative': 1200, 'size': 110}
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id: 166467308
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 66, 'group_counter': 28, 'group_order': 66550, 'label': '11D-2', 'order': 11, 'powers': [70, 63, 1], 'representative': 54570, 'size': 110}
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id: 166467309
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 67, 'group_counter': 28, 'group_order': 66550, 'label': '11D3', 'order': 11, 'powers': [72, 69, 1], 'representative': 12580, 'size': 110}
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id: 166467310
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 68, 'group_counter': 28, 'group_order': 66550, 'label': '11D-3', 'order': 11, 'powers': [71, 70, 1], 'representative': 61340, 'size': 110}
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id: 166467311
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 69, 'group_counter': 28, 'group_order': 66550, 'label': '11D4', 'order': 11, 'powers': [68, 66, 1], 'representative': 55530, 'size': 110}
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id: 166467313
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 70, 'group_counter': 28, 'group_order': 66550, 'label': '11D-4', 'order': 11, 'powers': [67, 65, 1], 'representative': 30490, 'size': 110}
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id: 166467314
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 71, 'group_counter': 28, 'group_order': 66550, 'label': '11D5', 'order': 11, 'powers': [64, 67, 1], 'representative': 60860, 'size': 110}
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id: 166467315
{'aut_label': '11D1', 'centralizer': '110.d1.a1', 'counter': 72, 'group_counter': 28, 'group_order': 66550, 'label': '11D-5', 'order': 11, 'powers': [63, 68, 1], 'representative': 31210, 'size': 110}
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id: 166467316
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 73, 'group_counter': 28, 'group_order': 66550, 'label': '22A1', 'order': 22, 'powers': [52, 77, 2], 'representative': 5, 'size': 121}
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id: 166467317
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 74, 'group_counter': 28, 'group_order': 66550, 'label': '22A-1', 'order': 22, 'powers': [53, 78, 2], 'representative': 105, 'size': 121}
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id: 166467318
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 75, 'group_counter': 28, 'group_order': 66550, 'label': '22A3', 'order': 22, 'powers': [56, 80, 2], 'representative': 15, 'size': 121}
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id: 166467319
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 76, 'group_counter': 28, 'group_order': 66550, 'label': '22A-3', 'order': 22, 'powers': [57, 79, 2], 'representative': 95, 'size': 121}
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id: 166467320
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 77, 'group_counter': 28, 'group_order': 66550, 'label': '22A5', 'order': 22, 'powers': [60, 75, 2], 'representative': 25, 'size': 121}
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id: 166467321
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 78, 'group_counter': 28, 'group_order': 66550, 'label': '22A-5', 'order': 22, 'powers': [61, 76, 2], 'representative': 85, 'size': 121}
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id: 166467322
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 79, 'group_counter': 28, 'group_order': 66550, 'label': '22A7', 'order': 22, 'powers': [59, 82, 2], 'representative': 35, 'size': 121}
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id: 166467324
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 80, 'group_counter': 28, 'group_order': 66550, 'label': '22A-7', 'order': 22, 'powers': [58, 81, 2], 'representative': 75, 'size': 121}
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id: 166467325
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 81, 'group_counter': 28, 'group_order': 66550, 'label': '22A9', 'order': 22, 'powers': [55, 73, 2], 'representative': 45, 'size': 121}
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id: 166467326
{'aut_label': '22A1', 'centralizer': '121.a1.a1', 'counter': 82, 'group_counter': 28, 'group_order': 66550, 'label': '22A-9', 'order': 22, 'powers': [54, 74, 2], 'representative': 65, 'size': 121}
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id: 166467327
{'aut_label': '55A1', 'centralizer': '10.a1.a1', 'counter': 83, 'group_counter': 28, 'group_order': 66550, 'label': '55A1', 'order': 55, 'powers': [85, 51, 3], 'representative': 1210, 'size': 10}
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id: 166467328
{'aut_label': '55A1', 'centralizer': '10.a1.a1', 'counter': 84, 'group_counter': 28, 'group_order': 66550, 'label': '55A-1', 'order': 55, 'powers': [86, 51, 4], 'representative': 4840, 'size': 10}
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id: 166467329
{'aut_label': '55A1', 'centralizer': '10.a1.a1', 'counter': 85, 'group_counter': 28, 'group_order': 66550, 'label': '55A2', 'order': 55, 'powers': [84, 51, 5], 'representative': 2420, 'size': 10}
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id: 166467330
{'aut_label': '55A1', 'centralizer': '10.a1.a1', 'counter': 86, 'group_counter': 28, 'group_order': 66550, 'label': '55A-2', 'order': 55, 'powers': [83, 51, 6], 'representative': 3630, 'size': 10}
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id: 166467331
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 87, 'group_counter': 28, 'group_order': 66550, 'label': '55B1', 'order': 55, 'powers': [89, 60, 5], 'representative': 26630, 'size': 11}
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id: 166467332
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 88, 'group_counter': 28, 'group_order': 66550, 'label': '55B-1', 'order': 55, 'powers': [90, 61, 6], 'representative': 40030, 'size': 11}
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id: 166467333
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 89, 'group_counter': 28, 'group_order': 66550, 'label': '55B2', 'order': 55, 'powers': [93, 53, 4], 'representative': 53260, 'size': 11}
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id: 166467335
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 90, 'group_counter': 28, 'group_order': 66550, 'label': '55B-2', 'order': 55, 'powers': [94, 52, 3], 'representative': 13400, 'size': 11}
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id: 166467336
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 91, 'group_counter': 28, 'group_order': 66550, 'label': '55B3', 'order': 55, 'powers': [95, 58, 3], 'representative': 13340, 'size': 11}
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id: 166467337
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 92, 'group_counter': 28, 'group_order': 66550, 'label': '55B-3', 'order': 55, 'powers': [96, 59, 4], 'representative': 53320, 'size': 11}
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id: 166467338
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 93, 'group_counter': 28, 'group_order': 66550, 'label': '55B4', 'order': 55, 'powers': [99, 55, 6], 'representative': 39970, 'size': 11}
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id: 166467339
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 94, 'group_counter': 28, 'group_order': 66550, 'label': '55B-4', 'order': 55, 'powers': [100, 54, 5], 'representative': 26690, 'size': 11}
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id: 166467340
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 95, 'group_counter': 28, 'group_order': 66550, 'label': '55B6', 'order': 55, 'powers': [103, 57, 5], 'representative': 26680, 'size': 11}
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id: 166467341
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 96, 'group_counter': 28, 'group_order': 66550, 'label': '55B-6', 'order': 55, 'powers': [104, 56, 6], 'representative': 39980, 'size': 11}
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id: 166467342
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 97, 'group_counter': 28, 'group_order': 66550, 'label': '55B7', 'order': 55, 'powers': [107, 54, 4], 'representative': 53310, 'size': 11}
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id: 166467343
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 98, 'group_counter': 28, 'group_order': 66550, 'label': '55B-7', 'order': 55, 'powers': [108, 55, 3], 'representative': 13350, 'size': 11}
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id: 166467344
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 99, 'group_counter': 28, 'group_order': 66550, 'label': '55B8', 'order': 55, 'powers': [109, 59, 3], 'representative': 13390, 'size': 11}
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id: 166466737
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 100, 'group_counter': 28, 'group_order': 66550, 'label': '55B-8', 'order': 55, 'powers': [110, 58, 4], 'representative': 53270, 'size': 11}
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id: 166466738
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 101, 'group_counter': 28, 'group_order': 66550, 'label': '55B9', 'order': 55, 'powers': [113, 52, 6], 'representative': 40020, 'size': 11}
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id: 166466739
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 102, 'group_counter': 28, 'group_order': 66550, 'label': '55B-9', 'order': 55, 'powers': [114, 53, 5], 'representative': 26640, 'size': 11}
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id: 166466740
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 103, 'group_counter': 28, 'group_order': 66550, 'label': '55B12', 'order': 55, 'powers': [121, 60, 4], 'representative': 53250, 'size': 11}
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id: 166466741
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 104, 'group_counter': 28, 'group_order': 66550, 'label': '55B-12', 'order': 55, 'powers': [122, 61, 3], 'representative': 13410, 'size': 11}
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id: 166466742
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 105, 'group_counter': 28, 'group_order': 66550, 'label': '55B13', 'order': 55, 'powers': [123, 53, 3], 'representative': 13330, 'size': 11}
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id: 166466743
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 106, 'group_counter': 28, 'group_order': 66550, 'label': '55B-13', 'order': 55, 'powers': [124, 52, 4], 'representative': 53330, 'size': 11}
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id: 166466744
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 107, 'group_counter': 28, 'group_order': 66550, 'label': '55B14', 'order': 55, 'powers': [126, 58, 6], 'representative': 39960, 'size': 11}
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id: 166466745
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 108, 'group_counter': 28, 'group_order': 66550, 'label': '55B-14', 'order': 55, 'powers': [125, 59, 5], 'representative': 26700, 'size': 11}
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id: 166466746
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 109, 'group_counter': 28, 'group_order': 66550, 'label': '55B16', 'order': 55, 'powers': [120, 56, 5], 'representative': 26670, 'size': 11}
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id: 166466748
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 110, 'group_counter': 28, 'group_order': 66550, 'label': '55B-16', 'order': 55, 'powers': [119, 57, 6], 'representative': 39990, 'size': 11}
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id: 166466749
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 111, 'group_counter': 28, 'group_order': 66550, 'label': '55B17', 'order': 55, 'powers': [118, 57, 4], 'representative': 53300, 'size': 11}
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id: 166466750
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 112, 'group_counter': 28, 'group_order': 66550, 'label': '55B-17', 'order': 55, 'powers': [117, 56, 3], 'representative': 13360, 'size': 11}
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id: 166466751
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id: 166466752
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id: 166466753
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 115, 'group_counter': 28, 'group_order': 66550, 'label': '55B19', 'order': 55, 'powers': [112, 59, 6], 'representative': 40010, 'size': 11}
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id: 166466754
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 116, 'group_counter': 28, 'group_order': 66550, 'label': '55B-19', 'order': 55, 'powers': [111, 58, 5], 'representative': 26650, 'size': 11}
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id: 166466755
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 117, 'group_counter': 28, 'group_order': 66550, 'label': '55B21', 'order': 55, 'powers': [106, 61, 5], 'representative': 26720, 'size': 11}
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id: 166466756
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 118, 'group_counter': 28, 'group_order': 66550, 'label': '55B-21', 'order': 55, 'powers': [105, 60, 6], 'representative': 39940, 'size': 11}
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id: 166466757
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id: 166466759
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 120, 'group_counter': 28, 'group_order': 66550, 'label': '55B-23', 'order': 55, 'powers': [101, 61, 4], 'representative': 53340, 'size': 11}
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id: 166466760
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 121, 'group_counter': 28, 'group_order': 66550, 'label': '55B24', 'order': 55, 'powers': [98, 53, 6], 'representative': 39950, 'size': 11}
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id: 166466761
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id: 166466762
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 123, 'group_counter': 28, 'group_order': 66550, 'label': '55B26', 'order': 55, 'powers': [92, 55, 5], 'representative': 26660, 'size': 11}
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id: 166466763
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 124, 'group_counter': 28, 'group_order': 66550, 'label': '55B-26', 'order': 55, 'powers': [91, 54, 6], 'representative': 40000, 'size': 11}
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id: 166466764
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 125, 'group_counter': 28, 'group_order': 66550, 'label': '55B27', 'order': 55, 'powers': [88, 56, 4], 'representative': 53290, 'size': 11}
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id: 166466765
{'aut_label': '55B1', 'centralizer': '11.b1.a1', 'counter': 126, 'group_counter': 28, 'group_order': 66550, 'label': '55B-27', 'order': 55, 'powers': [87, 57, 3], 'representative': 13370, 'size': 11}
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id: 166466766
{'aut_label': '55C1', 'centralizer': '110.b1.a1', 'counter': 127, 'group_counter': 28, 'group_order': 66550, 'label': '55C1', 'order': 55, 'powers': [129, 62, 3], 'representative': 1320, 'size': 110}
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id: 166466767
{'aut_label': '55C1', 'centralizer': '110.b1.a1', 'counter': 128, 'group_counter': 28, 'group_order': 66550, 'label': '55C-1', 'order': 55, 'powers': [130, 62, 4], 'representative': 4950, 'size': 110}
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id: 166466768
{'aut_label': '55C1', 'centralizer': '110.b1.a1', 'counter': 129, 'group_counter': 28, 'group_order': 66550, 'label': '55C2', 'order': 55, 'powers': [128, 62, 5], 'representative': 2530, 'size': 110}
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id: 166466770
{'aut_label': '55C1', 'centralizer': '110.b1.a1', 'counter': 130, 'group_counter': 28, 'group_order': 66550, 'label': '55C-2', 'order': 55, 'powers': [127, 62, 6], 'representative': 3740, 'size': 110}
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id: 166466771
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 131, 'group_counter': 28, 'group_order': 66550, 'label': '55D1', 'order': 55, 'powers': [133, 63, 3], 'representative': 1330, 'size': 110}
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id: 166466772
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 132, 'group_counter': 28, 'group_order': 66550, 'label': '55D-1', 'order': 55, 'powers': [134, 64, 4], 'representative': 5050, 'size': 110}
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id: 166466773
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 133, 'group_counter': 28, 'group_order': 66550, 'label': '55D2', 'order': 55, 'powers': [137, 65, 5], 'representative': 2550, 'size': 110}
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id: 166466774
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 134, 'group_counter': 28, 'group_order': 66550, 'label': '55D-2', 'order': 55, 'powers': [138, 66, 6], 'representative': 3830, 'size': 110}
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id: 166466775
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 135, 'group_counter': 28, 'group_order': 66550, 'label': '55D3', 'order': 55, 'powers': [139, 67, 6], 'representative': 3770, 'size': 110}
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id: 166466776
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 136, 'group_counter': 28, 'group_order': 66550, 'label': '55D-3', 'order': 55, 'powers': [140, 68, 5], 'representative': 2610, 'size': 110}
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id: 166466777
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 137, 'group_counter': 28, 'group_order': 66550, 'label': '55D4', 'order': 55, 'powers': [143, 69, 4], 'representative': 4990, 'size': 110}
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id: 166466778
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 138, 'group_counter': 28, 'group_order': 66550, 'label': '55D-4', 'order': 55, 'powers': [144, 70, 3], 'representative': 1390, 'size': 110}
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id: 166466779
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 139, 'group_counter': 28, 'group_order': 66550, 'label': '55D6', 'order': 55, 'powers': [147, 72, 3], 'representative': 1380, 'size': 110}
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id: 166466781
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 140, 'group_counter': 28, 'group_order': 66550, 'label': '55D-6', 'order': 55, 'powers': [148, 71, 4], 'representative': 5000, 'size': 110}
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id: 166466782
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 141, 'group_counter': 28, 'group_order': 66550, 'label': '55D7', 'order': 55, 'powers': [151, 70, 5], 'representative': 2600, 'size': 110}
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id: 166466783
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 142, 'group_counter': 28, 'group_order': 66550, 'label': '55D-7', 'order': 55, 'powers': [152, 69, 6], 'representative': 3780, 'size': 110}
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id: 166466784
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 143, 'group_counter': 28, 'group_order': 66550, 'label': '55D8', 'order': 55, 'powers': [153, 68, 6], 'representative': 3820, 'size': 110}
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id: 166466785
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 144, 'group_counter': 28, 'group_order': 66550, 'label': '55D-8', 'order': 55, 'powers': [154, 67, 5], 'representative': 2560, 'size': 110}
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id: 166466786
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 145, 'group_counter': 28, 'group_order': 66550, 'label': '55D9', 'order': 55, 'powers': [157, 66, 4], 'representative': 5040, 'size': 110}
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id: 166466787
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 146, 'group_counter': 28, 'group_order': 66550, 'label': '55D-9', 'order': 55, 'powers': [158, 65, 3], 'representative': 1340, 'size': 110}
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id: 166466788
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 147, 'group_counter': 28, 'group_order': 66550, 'label': '55D12', 'order': 55, 'powers': [165, 63, 5], 'representative': 2540, 'size': 110}
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id: 166466789
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 148, 'group_counter': 28, 'group_order': 66550, 'label': '55D-12', 'order': 55, 'powers': [166, 64, 6], 'representative': 3840, 'size': 110}
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id: 166466790
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 149, 'group_counter': 28, 'group_order': 66550, 'label': '55D13', 'order': 55, 'powers': [167, 65, 6], 'representative': 3760, 'size': 110}
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id: 166466792
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 150, 'group_counter': 28, 'group_order': 66550, 'label': '55D-13', 'order': 55, 'powers': [168, 66, 5], 'representative': 2620, 'size': 110}
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id: 166466793
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 151, 'group_counter': 28, 'group_order': 66550, 'label': '55D14', 'order': 55, 'powers': [170, 67, 4], 'representative': 4980, 'size': 110}
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id: 166466794
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 152, 'group_counter': 28, 'group_order': 66550, 'label': '55D-14', 'order': 55, 'powers': [169, 68, 3], 'representative': 1400, 'size': 110}
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id: 166466795
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 153, 'group_counter': 28, 'group_order': 66550, 'label': '55D16', 'order': 55, 'powers': [164, 71, 3], 'representative': 1370, 'size': 110}
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id: 166466796
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 154, 'group_counter': 28, 'group_order': 66550, 'label': '55D-16', 'order': 55, 'powers': [163, 72, 4], 'representative': 5010, 'size': 110}
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id: 166466797
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 155, 'group_counter': 28, 'group_order': 66550, 'label': '55D17', 'order': 55, 'powers': [162, 72, 5], 'representative': 2590, 'size': 110}
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id: 166466798
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 156, 'group_counter': 28, 'group_order': 66550, 'label': '55D-17', 'order': 55, 'powers': [161, 71, 6], 'representative': 3790, 'size': 110}
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id: 166466799
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 157, 'group_counter': 28, 'group_order': 66550, 'label': '55D18', 'order': 55, 'powers': [160, 70, 6], 'representative': 3810, 'size': 110}
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id: 166466800
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 158, 'group_counter': 28, 'group_order': 66550, 'label': '55D-18', 'order': 55, 'powers': [159, 69, 5], 'representative': 2570, 'size': 110}
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id: 166466801
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 159, 'group_counter': 28, 'group_order': 66550, 'label': '55D19', 'order': 55, 'powers': [156, 68, 4], 'representative': 5030, 'size': 110}
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id: 166466803
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 160, 'group_counter': 28, 'group_order': 66550, 'label': '55D-19', 'order': 55, 'powers': [155, 67, 3], 'representative': 1350, 'size': 110}
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id: 166466804
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 161, 'group_counter': 28, 'group_order': 66550, 'label': '55D21', 'order': 55, 'powers': [150, 64, 3], 'representative': 1420, 'size': 110}
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id: 166466805
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 162, 'group_counter': 28, 'group_order': 66550, 'label': '55D-21', 'order': 55, 'powers': [149, 63, 4], 'representative': 4960, 'size': 110}
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id: 166466806
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 163, 'group_counter': 28, 'group_order': 66550, 'label': '55D23', 'order': 55, 'powers': [146, 63, 6], 'representative': 3750, 'size': 110}
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id: 166466807
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 164, 'group_counter': 28, 'group_order': 66550, 'label': '55D-23', 'order': 55, 'powers': [145, 64, 5], 'representative': 2630, 'size': 110}
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id: 166466808
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 165, 'group_counter': 28, 'group_order': 66550, 'label': '55D24', 'order': 55, 'powers': [142, 65, 4], 'representative': 4970, 'size': 110}
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id: 166466809
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 166, 'group_counter': 28, 'group_order': 66550, 'label': '55D-24', 'order': 55, 'powers': [141, 66, 3], 'representative': 1410, 'size': 110}
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id: 166466810
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 167, 'group_counter': 28, 'group_order': 66550, 'label': '55D26', 'order': 55, 'powers': [136, 69, 3], 'representative': 1360, 'size': 110}
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id: 166466811
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 168, 'group_counter': 28, 'group_order': 66550, 'label': '55D-26', 'order': 55, 'powers': [135, 70, 4], 'representative': 5020, 'size': 110}
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id: 166466812
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 169, 'group_counter': 28, 'group_order': 66550, 'label': '55D27', 'order': 55, 'powers': [132, 71, 5], 'representative': 2580, 'size': 110}
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id: 166466814
{'aut_label': '55D1', 'centralizer': '110.d1.a1', 'counter': 170, 'group_counter': 28, 'group_order': 66550, 'label': '55D-27', 'order': 55, 'powers': [131, 72, 6], 'representative': 3800, 'size': 110}
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id: 166466815
{'aut_label': '55E1', 'centralizer': '121.a1.a1', 'counter': 171, 'group_counter': 28, 'group_order': 66550, 'label': '55E1', 'order': 55, 'powers': [173, 52, 7], 'representative': 2, 'size': 121}
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id: 166466816
{'aut_label': '55E-1', 'centralizer': '121.a1.a1', 'counter': 172, 'group_counter': 28, 'group_order': 66550, 'label': '55E-1', 'order': 55, 'powers': [174, 53, 8], 'representative': 108, 'size': 121}
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id: 166466817
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 173, 'group_counter': 28, 'group_order': 66550, 'label': '55E2', 'order': 55, 'powers': [177, 54, 9], 'representative': 4, 'size': 121}
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id: 166466818
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 174, 'group_counter': 28, 'group_order': 66550, 'label': '55E-2', 'order': 55, 'powers': [178, 55, 10], 'representative': 106, 'size': 121}
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id: 166466819
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 175, 'group_counter': 28, 'group_order': 66550, 'label': '55E3', 'order': 55, 'powers': [179, 56, 10], 'representative': 6, 'size': 121}
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id: 166466820
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 176, 'group_counter': 28, 'group_order': 66550, 'label': '55E-3', 'order': 55, 'powers': [180, 57, 9], 'representative': 104, 'size': 121}
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id: 166466821
{'aut_label': '55E-1', 'centralizer': '121.a1.a1', 'counter': 177, 'group_counter': 28, 'group_order': 66550, 'label': '55E4', 'order': 55, 'powers': [183, 58, 8], 'representative': 8, 'size': 121}
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id: 166466822
{'aut_label': '55E1', 'centralizer': '121.a1.a1', 'counter': 178, 'group_counter': 28, 'group_order': 66550, 'label': '55E-4', 'order': 55, 'powers': [184, 59, 7], 'representative': 102, 'size': 121}
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id: 166466823
{'aut_label': '55E1', 'centralizer': '121.a1.a1', 'counter': 179, 'group_counter': 28, 'group_order': 66550, 'label': '55E6', 'order': 55, 'powers': [187, 61, 7], 'representative': 12, 'size': 121}
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id: 166466825
{'aut_label': '55E-1', 'centralizer': '121.a1.a1', 'counter': 180, 'group_counter': 28, 'group_order': 66550, 'label': '55E-6', 'order': 55, 'powers': [188, 60, 8], 'representative': 98, 'size': 121}
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id: 166466826
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 181, 'group_counter': 28, 'group_order': 66550, 'label': '55E7', 'order': 55, 'powers': [191, 59, 9], 'representative': 14, 'size': 121}
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id: 166466827
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 182, 'group_counter': 28, 'group_order': 66550, 'label': '55E-7', 'order': 55, 'powers': [192, 58, 10], 'representative': 96, 'size': 121}
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id: 166466828
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 183, 'group_counter': 28, 'group_order': 66550, 'label': '55E8', 'order': 55, 'powers': [193, 57, 10], 'representative': 16, 'size': 121}
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id: 166466829
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 184, 'group_counter': 28, 'group_order': 66550, 'label': '55E-8', 'order': 55, 'powers': [194, 56, 9], 'representative': 94, 'size': 121}
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id: 166466830
{'aut_label': '55E-1', 'centralizer': '121.a1.a1', 'counter': 185, 'group_counter': 28, 'group_order': 66550, 'label': '55E9', 'order': 55, 'powers': [197, 55, 8], 'representative': 18, 'size': 121}
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id: 166466831
{'aut_label': '55E1', 'centralizer': '121.a1.a1', 'counter': 186, 'group_counter': 28, 'group_order': 66550, 'label': '55E-9', 'order': 55, 'powers': [198, 54, 7], 'representative': 92, 'size': 121}
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id: 166466832
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 187, 'group_counter': 28, 'group_order': 66550, 'label': '55E12', 'order': 55, 'powers': [205, 52, 9], 'representative': 24, 'size': 121}
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id: 166466833
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 188, 'group_counter': 28, 'group_order': 66550, 'label': '55E-12', 'order': 55, 'powers': [206, 53, 10], 'representative': 86, 'size': 121}
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id: 166466834
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 189, 'group_counter': 28, 'group_order': 66550, 'label': '55E13', 'order': 55, 'powers': [207, 54, 10], 'representative': 26, 'size': 121}
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id: 166466836
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 190, 'group_counter': 28, 'group_order': 66550, 'label': '55E-13', 'order': 55, 'powers': [208, 55, 9], 'representative': 84, 'size': 121}
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id: 166466837
{'aut_label': '55E-1', 'centralizer': '121.a1.a1', 'counter': 191, 'group_counter': 28, 'group_order': 66550, 'label': '55E14', 'order': 55, 'powers': [210, 56, 8], 'representative': 28, 'size': 121}
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id: 166466838
{'aut_label': '55E1', 'centralizer': '121.a1.a1', 'counter': 192, 'group_counter': 28, 'group_order': 66550, 'label': '55E-14', 'order': 55, 'powers': [209, 57, 7], 'representative': 82, 'size': 121}
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id: 166466839
{'aut_label': '55E1', 'centralizer': '121.a1.a1', 'counter': 193, 'group_counter': 28, 'group_order': 66550, 'label': '55E16', 'order': 55, 'powers': [204, 60, 7], 'representative': 32, 'size': 121}
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id: 166466840
{'aut_label': '55E-1', 'centralizer': '121.a1.a1', 'counter': 194, 'group_counter': 28, 'group_order': 66550, 'label': '55E-16', 'order': 55, 'powers': [203, 61, 8], 'representative': 78, 'size': 121}
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id: 166466841
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 195, 'group_counter': 28, 'group_order': 66550, 'label': '55E17', 'order': 55, 'powers': [202, 61, 9], 'representative': 34, 'size': 121}
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id: 166466842
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 196, 'group_counter': 28, 'group_order': 66550, 'label': '55E-17', 'order': 55, 'powers': [201, 60, 10], 'representative': 76, 'size': 121}
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id: 166466843
{'aut_label': '55E-2', 'centralizer': '121.a1.a1', 'counter': 197, 'group_counter': 28, 'group_order': 66550, 'label': '55E18', 'order': 55, 'powers': [200, 59, 10], 'representative': 36, 'size': 121}
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id: 166466844
{'aut_label': '55E2', 'centralizer': '121.a1.a1', 'counter': 198, 'group_counter': 28, 'group_order': 66550, 'label': '55E-18', 'order': 55, 'powers': [199, 58, 9], 'representative': 74, 'size': 121}
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id: 166466845
{'aut_label': '55E-1', 'centralizer': '121.a1.a1', 'counter': 199, 'group_counter': 28, 'group_order': 66550, 'label': '55E19', 'order': 55, 'powers': [196, 57, 8], 'representative': 38, 'size': 121}
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id: 166466848
{'aut_label': '55E1', 'centralizer': '121.a1.a1', 'counter': 200, 'group_counter': 28, 'group_order': 66550, 'label': '55E-19', 'order': 55, 'powers': [195, 56, 7], 'representative': 72, 'size': 121}
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id: 166466849
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id: 166467238
{'aut_label': '110A1', 'centralizer': '121.a1.a1', 'counter': 552, 'group_counter': 28, 'group_order': 66550, 'label': '110E-29', 'order': 110, 'powers': [367, 80, 43], 'representative': 4921, 'size': 121}
-
id: 166467239
{'aut_label': '110A1', 'centralizer': '121.a1.a1', 'counter': 553, 'group_counter': 28, 'group_order': 66550, 'label': '110E31', 'order': 110, 'powers': [366, 81, 43], 'representative': 4871, 'size': 121}
-
id: 166467240
{'aut_label': '110A-1', 'centralizer': '121.a1.a1', 'counter': 554, 'group_counter': 28, 'group_order': 66550, 'label': '110E-31', 'order': 110, 'powers': [365, 82, 44], 'representative': 1289, 'size': 121}
-
id: 166467241
{'aut_label': '110A-3', 'centralizer': '121.a1.a1', 'counter': 555, 'group_counter': 28, 'group_order': 66550, 'label': '110E37', 'order': 110, 'powers': [358, 80, 46], 'representative': 3667, 'size': 121}
-
id: 166467242
{'aut_label': '110A3', 'centralizer': '121.a1.a1', 'counter': 556, 'group_counter': 28, 'group_order': 66550, 'label': '110E-37', 'order': 110, 'powers': [357, 79, 45], 'representative': 2493, 'size': 121}
-
id: 166467243
{'aut_label': '110A-1', 'centralizer': '121.a1.a1', 'counter': 557, 'group_counter': 28, 'group_order': 66550, 'label': '110E39', 'order': 110, 'powers': [354, 78, 44], 'representative': 1249, 'size': 121}
-
id: 166467244
{'aut_label': '110A1', 'centralizer': '121.a1.a1', 'counter': 558, 'group_counter': 28, 'group_order': 66550, 'label': '110E-39', 'order': 110, 'powers': [353, 77, 43], 'representative': 4911, 'size': 121}
-
id: 166467245
{'aut_label': '110A1', 'centralizer': '121.a1.a1', 'counter': 559, 'group_counter': 28, 'group_order': 66550, 'label': '110E41', 'order': 110, 'powers': [352, 76, 43], 'representative': 4881, 'size': 121}
-
id: 166467247
{'aut_label': '110A-1', 'centralizer': '121.a1.a1', 'counter': 560, 'group_counter': 28, 'group_order': 66550, 'label': '110E-41', 'order': 110, 'powers': [351, 75, 44], 'representative': 1279, 'size': 121}
-
id: 166467248
{'aut_label': '110A3', 'centralizer': '121.a1.a1', 'counter': 561, 'group_counter': 28, 'group_order': 66550, 'label': '110E43', 'order': 110, 'powers': [348, 74, 45], 'representative': 2463, 'size': 121}
-
id: 166467249
{'aut_label': '110A-3', 'centralizer': '121.a1.a1', 'counter': 562, 'group_counter': 28, 'group_order': 66550, 'label': '110E-43', 'order': 110, 'powers': [347, 73, 46], 'representative': 3697, 'size': 121}
-
id: 166467250
{'aut_label': '110A-3', 'centralizer': '121.a1.a1', 'counter': 563, 'group_counter': 28, 'group_order': 66550, 'label': '110E47', 'order': 110, 'powers': [344, 75, 46], 'representative': 3677, 'size': 121}
-
id: 166467251
{'aut_label': '110A3', 'centralizer': '121.a1.a1', 'counter': 564, 'group_counter': 28, 'group_order': 66550, 'label': '110E-47', 'order': 110, 'powers': [343, 76, 45], 'representative': 2483, 'size': 121}
-
id: 166467252
{'aut_label': '110A-1', 'centralizer': '121.a1.a1', 'counter': 565, 'group_counter': 28, 'group_order': 66550, 'label': '110E49', 'order': 110, 'powers': [340, 77, 44], 'representative': 1259, 'size': 121}
-
id: 166467253
{'aut_label': '110A1', 'centralizer': '121.a1.a1', 'counter': 566, 'group_counter': 28, 'group_order': 66550, 'label': '110E-49', 'order': 110, 'powers': [339, 78, 43], 'representative': 4901, 'size': 121}
-
id: 166467254
{'aut_label': '110A1', 'centralizer': '121.a1.a1', 'counter': 567, 'group_counter': 28, 'group_order': 66550, 'label': '110E51', 'order': 110, 'powers': [338, 79, 43], 'representative': 4891, 'size': 121}
-
id: 166467255
{'aut_label': '110A-1', 'centralizer': '121.a1.a1', 'counter': 568, 'group_counter': 28, 'group_order': 66550, 'label': '110E-51', 'order': 110, 'powers': [337, 80, 44], 'representative': 1269, 'size': 121}
-
id: 166467256
{'aut_label': '110A3', 'centralizer': '121.a1.a1', 'counter': 569, 'group_counter': 28, 'group_order': 66550, 'label': '110E53', 'order': 110, 'powers': [334, 81, 45], 'representative': 2473, 'size': 121}
-
id: 166467258
{'aut_label': '110A-3', 'centralizer': '121.a1.a1', 'counter': 570, 'group_counter': 28, 'group_order': 66550, 'label': '110E-53', 'order': 110, 'powers': [333, 82, 46], 'representative': 3687, 'size': 121}
-
id: 166467259
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 571, 'group_counter': 28, 'group_order': 66550, 'label': '110F1', 'order': 110, 'powers': [87, 77, 47], 'representative': 1215, 'size': 121}
-
id: 166467260
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 572, 'group_counter': 28, 'group_order': 66550, 'label': '110F-1', 'order': 110, 'powers': [88, 78, 48], 'representative': 4945, 'size': 121}
-
id: 166467261
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 573, 'group_counter': 28, 'group_order': 66550, 'label': '110F3', 'order': 110, 'powers': [91, 80, 49], 'representative': 3645, 'size': 121}
-
id: 166467262
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 574, 'group_counter': 28, 'group_order': 66550, 'label': '110F-3', 'order': 110, 'powers': [92, 79, 50], 'representative': 2515, 'size': 121}
-
id: 166467263
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 575, 'group_counter': 28, 'group_order': 66550, 'label': '110F7', 'order': 110, 'powers': [97, 82, 50], 'representative': 2455, 'size': 121}
-
id: 166467264
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 576, 'group_counter': 28, 'group_order': 66550, 'label': '110F-7', 'order': 110, 'powers': [98, 81, 49], 'representative': 3705, 'size': 121}
-
id: 166467265
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 577, 'group_counter': 28, 'group_order': 66550, 'label': '110F9', 'order': 110, 'powers': [101, 73, 48], 'representative': 4885, 'size': 121}
-
id: 166467266
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 578, 'group_counter': 28, 'group_order': 66550, 'label': '110F-9', 'order': 110, 'powers': [102, 74, 47], 'representative': 1275, 'size': 121}
-
id: 166467267
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 579, 'group_counter': 28, 'group_order': 66550, 'label': '110F13', 'order': 110, 'powers': [105, 74, 49], 'representative': 3695, 'size': 121}
-
id: 166467269
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 580, 'group_counter': 28, 'group_order': 66550, 'label': '110F-13', 'order': 110, 'powers': [106, 73, 50], 'representative': 2465, 'size': 121}
-
id: 166467270
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 581, 'group_counter': 28, 'group_order': 66550, 'label': '110F17', 'order': 110, 'powers': [111, 76, 50], 'representative': 2505, 'size': 121}
-
id: 166467271
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 582, 'group_counter': 28, 'group_order': 66550, 'label': '110F-17', 'order': 110, 'powers': [112, 75, 49], 'representative': 3655, 'size': 121}
-
id: 166467272
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 583, 'group_counter': 28, 'group_order': 66550, 'label': '110F19', 'order': 110, 'powers': [115, 79, 48], 'representative': 4935, 'size': 121}
-
id: 166467273
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 584, 'group_counter': 28, 'group_order': 66550, 'label': '110F-19', 'order': 110, 'powers': [116, 80, 47], 'representative': 1225, 'size': 121}
-
id: 166467274
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 585, 'group_counter': 28, 'group_order': 66550, 'label': '110F21', 'order': 110, 'powers': [117, 78, 47], 'representative': 1315, 'size': 121}
-
id: 166467275
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 586, 'group_counter': 28, 'group_order': 66550, 'label': '110F-21', 'order': 110, 'powers': [118, 77, 48], 'representative': 4845, 'size': 121}
-
id: 166467276
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 587, 'group_counter': 28, 'group_order': 66550, 'label': '110F23', 'order': 110, 'powers': [119, 77, 49], 'representative': 3635, 'size': 121}
-
id: 166467277
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 588, 'group_counter': 28, 'group_order': 66550, 'label': '110F-23', 'order': 110, 'powers': [120, 78, 50], 'representative': 2525, 'size': 121}
-
id: 166467278
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 589, 'group_counter': 28, 'group_order': 66550, 'label': '110F27', 'order': 110, 'powers': [125, 75, 50], 'representative': 2445, 'size': 121}
-
id: 166467280
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 590, 'group_counter': 28, 'group_order': 66550, 'label': '110F-27', 'order': 110, 'powers': [126, 76, 49], 'representative': 3715, 'size': 121}
-
id: 166467281
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 591, 'group_counter': 28, 'group_order': 66550, 'label': '110F29', 'order': 110, 'powers': [124, 82, 48], 'representative': 4875, 'size': 121}
-
id: 166467282
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 592, 'group_counter': 28, 'group_order': 66550, 'label': '110F-29', 'order': 110, 'powers': [123, 81, 47], 'representative': 1285, 'size': 121}
-
id: 166467283
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 593, 'group_counter': 28, 'group_order': 66550, 'label': '110F31', 'order': 110, 'powers': [122, 73, 47], 'representative': 1255, 'size': 121}
-
id: 166467284
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 594, 'group_counter': 28, 'group_order': 66550, 'label': '110F-31', 'order': 110, 'powers': [121, 74, 48], 'representative': 4905, 'size': 121}
-
id: 166467285
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 595, 'group_counter': 28, 'group_order': 66550, 'label': '110F37', 'order': 110, 'powers': [114, 81, 50], 'representative': 2495, 'size': 121}
-
id: 166467286
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 596, 'group_counter': 28, 'group_order': 66550, 'label': '110F-37', 'order': 110, 'powers': [113, 82, 49], 'representative': 3665, 'size': 121}
-
id: 166467287
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 597, 'group_counter': 28, 'group_order': 66550, 'label': '110F39', 'order': 110, 'powers': [110, 76, 48], 'representative': 4925, 'size': 121}
-
id: 166467288
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 598, 'group_counter': 28, 'group_order': 66550, 'label': '110F-39', 'order': 110, 'powers': [109, 75, 47], 'representative': 1235, 'size': 121}
-
id: 166467289
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 599, 'group_counter': 28, 'group_order': 66550, 'label': '110F41', 'order': 110, 'powers': [108, 79, 47], 'representative': 1305, 'size': 121}
-
id: 166467292
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 600, 'group_counter': 28, 'group_order': 66550, 'label': '110F-41', 'order': 110, 'powers': [107, 80, 48], 'representative': 4855, 'size': 121}
-
id: 166467293
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 601, 'group_counter': 28, 'group_order': 66550, 'label': '110F43', 'order': 110, 'powers': [104, 78, 49], 'representative': 3735, 'size': 121}
-
id: 166467294
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 602, 'group_counter': 28, 'group_order': 66550, 'label': '110F-43', 'order': 110, 'powers': [103, 77, 50], 'representative': 2425, 'size': 121}
-
id: 166467295
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 603, 'group_counter': 28, 'group_order': 66550, 'label': '110F47', 'order': 110, 'powers': [100, 80, 50], 'representative': 2435, 'size': 121}
-
id: 166467296
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 604, 'group_counter': 28, 'group_order': 66550, 'label': '110F-47', 'order': 110, 'powers': [99, 79, 49], 'representative': 3725, 'size': 121}
-
id: 166467297
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 605, 'group_counter': 28, 'group_order': 66550, 'label': '110F49', 'order': 110, 'powers': [96, 75, 48], 'representative': 4865, 'size': 121}
-
id: 166467298
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 606, 'group_counter': 28, 'group_order': 66550, 'label': '110F-49', 'order': 110, 'powers': [95, 76, 47], 'representative': 1295, 'size': 121}
-
id: 166467299
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 607, 'group_counter': 28, 'group_order': 66550, 'label': '110F51', 'order': 110, 'powers': [94, 82, 47], 'representative': 1245, 'size': 121}
-
id: 166467300
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 608, 'group_counter': 28, 'group_order': 66550, 'label': '110F-51', 'order': 110, 'powers': [93, 81, 48], 'representative': 4915, 'size': 121}
-
id: 166467301
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 609, 'group_counter': 28, 'group_order': 66550, 'label': '110F53', 'order': 110, 'powers': [90, 73, 49], 'representative': 3675, 'size': 121}
-
id: 166467303
{'aut_label': '110F1', 'centralizer': '121.a1.a1', 'counter': 610, 'group_counter': 28, 'group_order': 66550, 'label': '110F-53', 'order': 110, 'powers': [89, 74, 50], 'representative': 2485, 'size': 121}
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gps_qchar • Show schema
Hide schema
-
id: 16647011
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '66550.bb', 'group_order': 66550, 'image': None, 'label': '66550.bb.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 16647023
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id: 16647024
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id: 16647025
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id: 16647026
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id: 16647034
{'cdim': 10, 'counter': 30, 'faithful': False, 'group': '66550.bb', 'group_order': 66550, 'image': None, 'label': '66550.bb.10b', 'multiplicity': 4, 'nt': [55, 0], 'qdim': 40, 'qvalues': [40, 0, -10, -10, -10, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 16647035
{'cdim': 10, 'counter': 31, 'faithful': False, 'group': '66550.bb', 'group_order': 66550, 'image': None, 'label': '66550.bb.10c', 'multiplicity': 10, 'nt': [110, 0], 'qdim': 100, 'qvalues': [100, 0, 100, 100, 100, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, 1, -10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 100, 100, 100, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -10, 1, 1, 1, 1, 1, 1, 1, -10, -10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 16647037
{'cdim': 110, 'counter': 33, 'faithful': False, 'group': '66550.bb', 'group_order': 66550, 'image': None, 'label': '66550.bb.110a', 'multiplicity': 1, 'nt': [121, 0], 'qdim': 110, 'qvalues': [110, 0, 110, 110, 110, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -11, -11, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 16647036
{'cdim': 10, 'counter': 32, 'faithful': False, 'group': '66550.bb', 'group_order': 66550, 'image': None, 'label': '66550.bb.10d', 'multiplicity': 40, 'nt': [550, 0], 'qdim': 400, 'qvalues': [400, 0, -100, -100, -100, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400, -40, -40, -40, -40, -40, -40, -40, -40, -40, -40, 4, -40, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, -100, -100, -100, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, 10, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 16647038
{'cdim': 110, 'counter': 34, 'faithful': True, 'group': '66550.bb', 'group_order': 66550, 'image': None, 'label': '66550.bb.110b', 'multiplicity': 4, 'nt': [605, 0], 'qdim': 440, 'qvalues': [440, 0, -110, -110, -110, -110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 11, 11, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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group 66550.bb does not appear in gps_char
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gps_subgroup_search • Show schema
Hide schema
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id: 242167009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 66550, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 110, 'label': '66550.bb.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '66550.bb', 'subgroup_hash': 1745369678053108262, 'subgroup_order': 66550, 'subgroup_tex': 'C_5\\times C_{11}^2:C_{110}', 'supersolvable': True, 'sylow': 0}
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id: 242167037
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 33275, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 55, 'label': '66550.bb.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33275.i', 'subgroup_hash': 6843608193946119759, 'subgroup_order': 33275, 'subgroup_tex': '\\He_{11}:C_5^2', 'supersolvable': True, 'sylow': 0}
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id: 242167048
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 13310, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '13310.bd', 'subgroup_hash': 5985541689969799654, 'subgroup_order': 13310, 'subgroup_tex': 'C_{11}^2:C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': True, 'centralizer_order': 5, 'characteristic': False, 'core_order': 13310, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '66550.bb.5.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '13310.bf', 'subgroup_hash': 7716340785735456673, 'subgroup_order': 13310, 'subgroup_tex': 'C_{11}^2:C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167070
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': True, 'centralizer_order': 5, 'characteristic': False, 'core_order': 13310, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '66550.bb.5.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '13310.bf', 'subgroup_hash': 7716340785735456673, 'subgroup_order': 13310, 'subgroup_tex': 'C_{11}^2:C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167081
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': True, 'centralizer_order': 5, 'characteristic': False, 'core_order': 13310, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '66550.bb.5.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '13310.bf', 'subgroup_hash': 7716340785735456673, 'subgroup_order': 13310, 'subgroup_tex': 'C_{11}^2:C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167092
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': True, 'centralizer_order': 5, 'characteristic': False, 'core_order': 13310, 'counter': 7, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '66550.bb.5.b1.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '13310.bf', 'subgroup_hash': 7716340785735456673, 'subgroup_order': 13310, 'subgroup_tex': 'C_{11}^2:C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167103
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': True, 'centralizer_order': 5, 'characteristic': False, 'core_order': 13310, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '66550.bb.5.b1.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '13310.bf', 'subgroup_hash': 7716340785735456673, 'subgroup_order': 13310, 'subgroup_tex': 'C_{11}^2:C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': True, 'core_order': 6655, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6655.4', 'subgroup_hash': 4, 'subgroup_order': 6655, 'subgroup_tex': 'C_5\\times \\He_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167010
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6655, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6655.23', 'subgroup_hash': 23, 'subgroup_order': 6655, 'subgroup_tex': 'C_{11}^2:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167021
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6655, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6655.23', 'subgroup_hash': 23, 'subgroup_order': 6655, 'subgroup_tex': 'C_{11}^2:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167029
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6655, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.10.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6655.23', 'subgroup_hash': 23, 'subgroup_order': 6655, 'subgroup_tex': 'C_{11}^2:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167030
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6655, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.10.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6655.23', 'subgroup_hash': 23, 'subgroup_order': 6655, 'subgroup_tex': 'C_{11}^2:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167031
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 6655, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.10.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6655.23', 'subgroup_hash': 23, 'subgroup_order': 6655, 'subgroup_tex': 'C_{11}^2:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167032
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 6050, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.11.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '11.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '11.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 11, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6050.a', 'subgroup_hash': 8547257569126712578, 'subgroup_order': 6050, 'subgroup_tex': 'C_{55}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167033
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 605, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.11.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6050.c', 'subgroup_hash': 6481451749276487661, 'subgroup_order': 6050, 'subgroup_tex': 'C_{55}\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167034
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 3025, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '22.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 22, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3025.d', 'subgroup_hash': 12, 'subgroup_order': 3025, 'subgroup_tex': 'C_{11}^2:C_5^2', 'supersolvable': True, 'sylow': 0}
-
id: 242167035
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 605, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '22.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3025.c', 'subgroup_hash': 11, 'subgroup_order': 3025, 'subgroup_tex': 'C_{55}:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167036
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 2662, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 22, 'label': '66550.bb.25.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '25.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '25.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 25, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2662.14', 'subgroup_hash': 14, 'subgroup_order': 2662, 'subgroup_tex': 'C_{11}^2:C_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 242167038
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': True, 'core_order': 1331, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 11, 'label': '66550.bb.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '50.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '50.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 50, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1331.3', 'subgroup_hash': 3, 'subgroup_order': 1331, 'subgroup_tex': '\\He_{11}', 'supersolvable': True, 'sylow': 11}
-
id: 242167039
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 1210, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '55.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '55.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.23', 'subgroup_hash': 23, 'subgroup_order': 1210, 'subgroup_tex': 'C_{55}:D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167040
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1210, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.55.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '55.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '55.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167041
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1210, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.55.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '55.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '55.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167042
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1210, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.55.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '55.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '55.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167043
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1210, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.55.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '55.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '55.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167044
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1210, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.55.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '55.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '55.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167045
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 605, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.55.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1210.22', 'subgroup_hash': 22, 'subgroup_order': 1210, 'subgroup_tex': 'D_{11}\\times C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167046
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.55.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1210.8', 'subgroup_hash': 8, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167047
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.55.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1210.8', 'subgroup_hash': 8, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167049
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.55.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1210.8', 'subgroup_hash': 8, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167050
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.55.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1210.8', 'subgroup_hash': 8, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167051
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.55.d1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '55.d1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1210.8', 'subgroup_hash': 8, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167052
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': True, 'core_order': 605, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.7', 'subgroup_hash': 7, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}\\times C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167053
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': True, 'core_order': 605, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.110.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '110.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.6', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{110}', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.7', 'subgroup_hash': 7, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}\\times C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167054
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 605, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.110.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '110.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.6', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{110}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.4', 'subgroup_hash': 4, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167055
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 605, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.110.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '110.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.6', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{110}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.4', 'subgroup_hash': 4, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167056
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 605, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.110.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '110.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.6', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{110}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.4', 'subgroup_hash': 4, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167057
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 605, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.110.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '110.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.6', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{110}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.4', 'subgroup_hash': 4, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167058
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 605, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.110.c1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '110.c1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.6', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{110}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.4', 'subgroup_hash': 4, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167060
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': False, 'core_order': 55, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.110.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '605.7', 'subgroup_hash': 7, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}\\times C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167061
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.110.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '605.3', 'subgroup_hash': 3, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167062
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.110.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '605.3', 'subgroup_hash': 3, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167063
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.110.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '605.3', 'subgroup_hash': 3, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167064
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.110.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '605.3', 'subgroup_hash': 3, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167065
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.110.e1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '110.e1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '605.3', 'subgroup_hash': 3, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}:C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167066
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 5, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.121.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '121.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 121, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '550.16', 'subgroup_hash': 16, 'subgroup_order': 550, 'subgroup_tex': 'C_5\\times C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167067
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 55, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.121.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '121.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 121, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '550.7', 'subgroup_hash': 7, 'subgroup_order': 550, 'subgroup_tex': 'C_5\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167068
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.121.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '121.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 121, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '550.7', 'subgroup_hash': 7, 'subgroup_order': 550, 'subgroup_tex': 'C_5\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167069
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 5, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.242.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 242, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '275.4', 'subgroup_hash': 4, 'subgroup_order': 275, 'subgroup_tex': 'C_5\\times C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167071
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 55, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.242.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '242.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 242, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '275.3', 'subgroup_hash': 3, 'subgroup_order': 275, 'subgroup_tex': 'C_{55}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167072
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.242.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '242.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 242, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '275.3', 'subgroup_hash': 3, 'subgroup_order': 275, 'subgroup_tex': 'C_{55}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167073
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': True, 'core_order': 242, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.275.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '275.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '275.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 275, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{55}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.4', 'subgroup_hash': 4, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}:D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167074
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 121, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.275.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '275.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 275, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '242.3', 'subgroup_hash': 3, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167075
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': True, 'core_order': 121, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.550.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '550.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '550.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 550, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times F_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '121.2', 'subgroup_hash': 2, 'subgroup_order': 121, 'subgroup_tex': 'C_{11}^2', 'supersolvable': True, 'sylow': 0}
-
id: 242167076
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': True, 'core_order': 121, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '66550.bb.550.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '550.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '550.16', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 550, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{110}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '121.2', 'subgroup_hash': 2, 'subgroup_order': 121, 'subgroup_tex': 'C_{11}^2', 'supersolvable': True, 'sylow': 0}
-
id: 242167077
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': False, 'core_order': 11, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.550.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '550.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 550, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '121.2', 'subgroup_hash': 2, 'subgroup_order': 121, 'subgroup_tex': 'C_{11}^2', 'supersolvable': True, 'sylow': 0}
-
id: 242167078
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 5, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.605.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.6', 'subgroup_hash': 6, 'subgroup_order': 110, 'subgroup_tex': 'C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167079
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.605.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.6', 'subgroup_hash': 6, 'subgroup_order': 110, 'subgroup_tex': 'C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167080
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.605.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.6', 'subgroup_hash': 6, 'subgroup_order': 110, 'subgroup_tex': 'C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167082
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.605.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.6', 'subgroup_hash': 6, 'subgroup_order': 110, 'subgroup_tex': 'C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167083
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.605.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.6', 'subgroup_hash': 6, 'subgroup_order': 110, 'subgroup_tex': 'C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167084
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.605.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.6', 'subgroup_hash': 6, 'subgroup_order': 110, 'subgroup_tex': 'C_{110}', 'supersolvable': True, 'sylow': 0}
-
id: 242167085
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 55, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.4', 'subgroup_hash': 4, 'subgroup_order': 110, 'subgroup_tex': 'C_5\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167086
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 5, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.4', 'subgroup_hash': 4, 'subgroup_order': 110, 'subgroup_tex': 'C_5\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167087
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167088
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167089
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167090
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167091
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.e1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.e1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167093
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167094
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167095
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167096
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167097
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.605.f1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '605.f1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167098
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 6655, 'characteristic': True, 'core_order': 55, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '66550.bb.1210.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1210.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1210.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1210, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}\\times F_{11}', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167099
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 6050, 'characteristic': False, 'core_order': 5, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167100
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': False, 'core_order': 5, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167101
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': False, 'core_order': 5, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167102
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167104
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167105
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167106
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167107
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.e1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.e1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
-
id: 242167108
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167109
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167110
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167111
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167112
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.f1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.f1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167113
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167115
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167116
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167117
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167118
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.1210.g1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1210.g1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167119
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 5, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '66550.bb.1331.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1331.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1331, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 242167120
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 5, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 5, 'label': '66550.bb.2662.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2662.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2662, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
-
id: 242167121
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.3025.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3025.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3025, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 242167122
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': False, 'core_order': 11, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.3025.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3025.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3025, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167123
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '66550.bb.3025.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3025.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3025, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167124
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 6655, 'characteristic': True, 'core_order': 11, 'counter': 99, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '66550.bb.6050.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '6050.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6050.c', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6481451749276487661, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6050, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}\\times F_{11}', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167011
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 6050, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6050.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6050.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167012
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6050.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6050.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167013
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 605, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6050.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6050.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6050, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 242167014
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 5, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6655.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6655.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6655, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 242167015
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6655.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6655.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6655, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 242167016
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6655.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6655.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6655, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 242167017
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6655.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6655.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6655, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 242167018
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6655.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6655.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6655, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 242167019
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.6655.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6655.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6655, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 242167020
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': True, 'central_factor': False, 'centralizer_order': 66550, 'characteristic': True, 'core_order': 5, 'counter': 109, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '66550.bb.13310.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '13310.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '13310.bf', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7716340785735456673, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 13310, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}^2:C_{110}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167022
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.13310.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13310.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13310, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167023
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.13310.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13310.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13310, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167024
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.13310.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13310.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13310, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167025
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.13310.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13310.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13310, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167026
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '66550.bb.13310.b1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13310.b1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 13310, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
-
id: 242167027
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': False, 'central_factor': False, 'centralizer_order': 550, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': True, 'direct': None, 'hall': 2, 'label': '66550.bb.33275.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '33275.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 33275, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 2}
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id: 242167028
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '66550.bb', 'ambient_counter': 28, 'ambient_order': 66550, 'ambient_tex': 'C_5\\times C_{11}^2:C_{110}', 'central': True, 'central_factor': False, 'centralizer_order': 66550, 'characteristic': True, 'core_order': 1, 'counter': 116, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '66550.bb.66550.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '66550.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '66550.bb', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1745369678053108262, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 66550, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{11}^2:C_{110}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 242167009
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['66550.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '5.a1.a1', '5.b1.a1', '5.b1.b1', '5.b1.c1', '5.b1.d1', '5.b1.e1', '11.a1.a1', '11.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5467, 3990, 6452, 4633, 3952, 4292, 4307, 5159], 'generators': [55, 6050, 13310, 10, 22, 110], 'label': '66550.bb.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '5.a1.a1', '5.b1.e1', '5.b1.c1', '5.b1.d1', '5.b1.a1', '5.b1.b1', '11.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
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id: 242167010
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['6655.a1.a1', '6655.b1.d1', '6655.b1.e1', '6655.b1.b1', '6655.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.b1.a1'], 'contains': ['50.a1.a1', '110.c1.a1', '110.e1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1632, 3836, 8686, 7448, 2257, 2092, 1690, 7631], 'generators': [22, 110, 6050, 10], 'label': '66550.bb.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.a1.a1', '5.b1.a1'], 'normal_contains': ['50.a1.a1', '110.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
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id: 242167011
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6050.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['550.a1.a1', '1210.b1.a1', '1210.e1.a1', '1210.e1.b1', '1210.e1.c1', '1210.e1.d1', '1210.e1.e1', '3025.a1.a1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3990, -1, 1139, -1, 7002, -1, 5447, -1], 'generators': [10], 'label': '66550.bb.6050.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '550.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '6050.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6050.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167012
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6050.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['550.b1.a1', '1210.c1.a1', '1210.g1.a1', '1210.g1.b1', '1210.g1.c1', '1210.g1.d1', '1210.g1.e1', '3025.c1.a1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9144, -1, 7174, -1, 3586, -1, 6759, -1], 'generators': [110], 'label': '66550.bb.6050.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '550.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '6050.c1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6050.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
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id: 242167013
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6050.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['550.c1.a1', '1210.d1.a1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [534, -1, 9604, -1, 1775, -1, 1081, -1], 'generators': [120], 'label': '66550.bb.6050.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '50.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.d1.a1', 'old_label': '6050.d1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6050.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167014
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6655.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['605.a1.a1', '605.c1.a1', '605.d1.a1', '1331.a1.a1'], 'contains': ['13310.a1.a1', '33275.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [7198, -1, 4254, -1, 6068, -1, 7797, -1], 'generators': [55, 13310], 'label': '66550.bb.6655.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '6655.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6655.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167015
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6655.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['605.b1.a1', '605.e1.a1', '605.f1.a1', '1331.a1.a1'], 'contains': ['13310.b1.a1', '33275.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5793, -1, 6425, -1, 6684, -1, 8129, -1], 'generators': [55, 22], 'label': '66550.bb.6655.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '6655.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6655.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167016
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6655.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['605.b1.b1', '605.e1.b1', '605.f1.b1', '1331.a1.a1'], 'contains': ['13310.b1.b1', '33275.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5793, -1, 2901, -1, 6684, -1, 7963, -1], 'generators': [60555, 2442], 'label': '66550.bb.6655.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '6655.b1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6655.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167017
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6655.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['605.b1.c1', '605.e1.c1', '605.f1.c1', '1331.a1.a1'], 'contains': ['13310.b1.c1', '33275.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5793, -1, 3558, -1, 6684, -1, 8296, -1], 'generators': [54505, 4862], 'label': '66550.bb.6655.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '6655.b1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6655.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167018
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6655.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['605.b1.d1', '605.e1.d1', '605.f1.d1', '1331.a1.a1'], 'contains': ['13310.b1.d1', '33275.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5793, -1, 3150, -1, 6684, -1, 8628, -1], 'generators': [30305, 1232], 'label': '66550.bb.6655.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '6655.b1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6655.b1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167019
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6655.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['605.b1.e1', '605.e1.e1', '605.f1.e1', '1331.a1.a1'], 'contains': ['13310.b1.e1', '33275.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5793, -1, 4872, -1, 6684, -1, 8462, -1], 'generators': [24255, 3652], 'label': '66550.bb.6655.b1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '6655.b1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6655.b1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167020
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '13310.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['5.b1.a1', '5.b1.b1', '5.b1.c1', '5.b1.d1', '5.b1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1210.a1.a1', '1210.b1.a1', '1210.c1.a1', '1210.d1.a1', '2662.a1.a1', '6655.a1.a1'], 'contains': ['66550.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6277, 6150, 7087, 9069, 5362, 7226, 5598, 8050], 'generators': [13310], 'label': '66550.bb.13310.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '13310.a1.a1', 'normal_contained_in': ['1210.a1.a1'], 'normal_contains': ['66550.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '13310.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '1.1', 'quotient_action_kernel': '13310.bf', 'quotient_action_kernel_order': 13310, 'quotient_fusion': None, 'short_label': '13310.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167021
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['6655.a1.a1', '6655.b1.e1', '6655.b1.a1', '6655.b1.c1', '6655.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.b1.b1'], 'contains': ['50.a1.a1', '110.c1.b1', '110.e1.b1'], 'core': '10.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1632, 3836, 6721, 5883, 2257, 2092, 1448, 8202], 'generators': [2442, 110, 6050, 10], 'label': '66550.bb.10.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.b1', 'normal_contained_in': ['2.a1.a1', '5.b1.b1'], 'normal_contains': ['50.a1.a1', '110.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '66550.bb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
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id: 242167022
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '13310.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1210.e1.a1', '1210.f1.a1', '1210.g1.a1', '2662.a1.a1', '6655.b1.a1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5127, -1, 6698, -1, 6206, -1, 5870, -1], 'generators': [22], 'label': '66550.bb.13310.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '13310.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13310.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167023
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '13310.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1210.e1.b1', '1210.f1.b1', '1210.g1.b1', '2662.a1.a1', '6655.b1.b1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5127, -1, 3458, -1, 6206, -1, 5734, -1], 'generators': [2442], 'label': '66550.bb.13310.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '13310.b1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13310.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167024
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '13310.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1210.e1.c1', '1210.f1.c1', '1210.g1.c1', '2662.a1.a1', '6655.b1.c1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5127, -1, 6030, -1, 6206, -1, 6006, -1], 'generators': [4862], 'label': '66550.bb.13310.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '13310.b1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13310.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167025
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '13310.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1210.e1.d1', '1210.f1.d1', '1210.g1.d1', '2662.a1.a1', '6655.b1.d1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5127, -1, 2778, -1, 6206, -1, 6278, -1], 'generators': [1232], 'label': '66550.bb.13310.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '13310.b1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13310.b1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167026
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '13310.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1210.e1.e1', '1210.f1.e1', '1210.g1.e1', '2662.a1.a1', '6655.b1.e1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5127, -1, 6281, -1, 6206, -1, 6142, -1], 'generators': [3652], 'label': '66550.bb.13310.b1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '13310.b1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13310.b1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167027
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '33275.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3025.a1.a1', '3025.b1.a1', '3025.c1.a1', '6655.a1.a1', '6655.b1.a1', '6655.b1.b1', '6655.b1.c1', '6655.b1.d1', '6655.b1.e1'], 'contains': ['66550.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5592, -1, 4404, -1, 5771, -1, 8046, -1], 'generators': [55], 'label': '66550.bb.33275.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '275.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '33275.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33275.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167028
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '66550.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6050.a1.a1', '6050.b1.a1', '6050.c1.a1', '6050.d1.a1', '13310.a1.a1', '13310.b1.a1', '13310.b1.b1', '13310.b1.c1', '13310.b1.d1', '13310.b1.e1', '33275.a1.a1'], 'contains': [], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5127, 5757, 6281, 8909, 5362, 6803, 5870, 7850], 'generators': [], 'label': '66550.bb.66550.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '66550.a1.a1', 'normal_contained_in': ['6050.a1.a1', '13310.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '66550.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66550.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167029
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['6655.a1.a1', '6655.b1.a1', '6655.b1.b1', '6655.b1.d1', '6655.b1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.b1.c1'], 'contains': ['50.a1.a1', '110.c1.c1', '110.e1.c1'], 'core': '10.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1632, 3836, 7562, 4353, 2257, 2092, 1932, 6489], 'generators': [4862, 110, 6050, 10], 'label': '66550.bb.10.b1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.c1', 'normal_contained_in': ['2.a1.a1', '5.b1.c1'], 'normal_contains': ['50.a1.a1', '110.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.c1', 'projective_image': '66550.bb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.c1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167030
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['6655.a1.a1', '6655.b1.b1', '6655.b1.c1', '6655.b1.e1', '6655.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.b1.d1'], 'contains': ['50.a1.a1', '110.c1.d1', '110.e1.d1'], 'core': '10.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1632, 3836, 5230, 2232, 2257, 2092, 2416, 7060], 'generators': [1232, 110, 6050, 10], 'label': '66550.bb.10.b1.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.d1', 'normal_contained_in': ['2.a1.a1', '5.b1.d1'], 'normal_contains': ['50.a1.a1', '110.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.d1', 'projective_image': '66550.bb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.d1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167031
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['6655.a1.a1', '6655.b1.c1', '6655.b1.d1', '6655.b1.a1', '6655.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.b1.e1'], 'contains': ['50.a1.a1', '110.c1.e1', '110.e1.e1'], 'core': '10.b1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [1632, 3836, 8394, 3401, 2257, 2092, 2174, 8773], 'generators': [3652, 110, 6050, 10], 'label': '66550.bb.10.b1.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.e1', 'normal_contained_in': ['2.a1.a1', '5.b1.e1'], 'normal_contains': ['50.a1.a1', '110.c1.e1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.e1', 'projective_image': '66550.bb', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1.e1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167032
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['6050.b1.a1', '6050.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '55.a1.a1', '55.b1.a1', '55.b1.b1', '55.b1.c1', '55.b1.d1', '55.b1.e1', '121.b1.a1', '121.c1.a1'], 'core': '11.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7529, 2166, 6269, 3200, 4673, 3136, 6797, 2545], 'generators': [55, 13310, 110, 22, 6050], 'label': '66550.bb.11.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '11.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['22.a1.a1', '55.a1.a1', '55.b1.e1', '55.b1.c1', '55.b1.d1', '55.b1.a1', '55.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '11.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167033
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '11.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.b1.a1', '55.c1.a1', '55.d1.a1', '55.d1.b1', '55.d1.c1', '55.d1.d1', '55.d1.e1', '121.a1.a1', '121.b1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5069, -1, 1504, -1, 6571, -1, 5218, -1], 'generators': [55, 13310, 10, 22, 6050], 'label': '66550.bb.11.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '11.b1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167034
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['3025.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['110.b1.a1', '110.c1.a1', '110.c1.b1', '110.c1.c1', '110.c1.d1', '110.c1.e1', '242.b1.a1', '242.c1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6772, 3695, 7856, 2800, 3680, 3709, 3159, 5151], 'generators': [22, 110, 6050, 13310], 'label': '66550.bb.22.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.a1.a1', '11.a1.a1'], 'normal_contains': ['110.b1.a1', '110.c1.e1', '110.c1.c1', '110.c1.d1', '110.c1.a1', '110.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '22.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167035
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.b1.a1'], 'contains': ['110.a1.a1', '110.e1.a1', '110.e1.b1', '110.e1.c1', '110.e1.d1', '110.e1.e1', '242.a1.a1', '242.b1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4034, -1, 3715, -1, 6944, -1, 2747, -1], 'generators': [22, 10, 6050, 13310], 'label': '66550.bb.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '22.b1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167036
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['2662.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '5.b1.a1', '5.b1.b1', '5.b1.c1', '5.b1.d1', '5.b1.e1'], 'contains': ['50.a1.a1', '275.a1.a1', '275.b1.a1'], 'core': '25.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1814, 5379, 7083, 6536, 1793, 5327, 3484, 5918], 'generators': [55, 110, 6050, 10], 'label': '66550.bb.25.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '25.a1.a1', 'normal_contained_in': ['5.a1.a1', '5.b1.e1', '5.b1.c1', '5.b1.d1', '5.b1.a1', '5.b1.b1'], 'normal_contains': ['50.a1.a1', '275.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '25.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '5.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '25.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167037
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['33275.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '10.b1.c1', '10.b1.d1', '10.b1.e1', '22.a1.a1', '22.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4034, 5000, 7578, 4215, 3217, 5458, 2174, 8224], 'generators': [22, 10, 110, 13310, 6050], 'label': '66550.bb.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.e1', '10.b1.c1', '10.b1.d1', '10.b1.a1', '10.b1.b1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167038
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.a1.a1', 'complements': ['1331.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '10.b1.c1', '10.b1.d1', '10.b1.e1', '25.a1.a1'], 'contains': ['550.a1.a1', '550.b1.a1', '550.c1.a1'], 'core': '50.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [971, 5379, 8688, 7144, 833, 5618, 435, 7631], 'generators': [10, 110], 'label': '66550.bb.50.a1.a1', 'mobius_quo': 0, 'mobius_sub': -5, 'normal_closure': '50.a1.a1', 'normal_contained_in': ['10.a1.a1', '10.b1.e1', '10.b1.c1', '10.b1.d1', '10.b1.a1', '10.b1.b1', '25.a1.a1'], 'normal_contains': ['550.a1.a1', '550.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '50.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '10.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '50.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.8'}
-
id: 242167039
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['1210.e1.a1', '1210.e1.d1', '1210.e1.b1', '1210.e1.e1', '1210.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.a1'], 'contains': ['110.b1.a1', '275.a1.a1', '605.c1.a1', '605.d1.a1'], 'core': '55.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7807, 5982, 6251, 7740, 2891, 6972, 5963, 4178], 'generators': [55, 110, 6050, 13310], 'label': '66550.bb.55.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '55.a1.a1', 'normal_contained_in': ['5.a1.a1', '11.a1.a1'], 'normal_contains': ['110.b1.a1', '275.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '55.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167040
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['1210.b1.a1', '1210.d1.a1', '1210.e1.d1', '1210.e1.e1', '1210.e1.b1', '1210.e1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['5.b1.a1', '11.a1.a1'], 'contains': ['110.c1.a1', '275.a1.a1', '605.e1.a1', '605.f1.a1'], 'core': '55.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5808, 1044, 8259, 5975, 4372, 700, 6953, 1822], 'generators': [55, 110, 6050, 22], 'label': '66550.bb.55.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '55.b1.a1', 'normal_contained_in': ['5.b1.a1', '11.a1.a1'], 'normal_contains': ['110.c1.a1', '275.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '55.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '11.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '55.b1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167041
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['1210.b1.a1', '1210.d1.a1', '1210.e1.e1', '1210.e1.a1', '1210.e1.c1', '1210.e1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['5.b1.b1', '11.a1.a1'], 'contains': ['110.c1.b1', '275.a1.a1', '605.e1.b1', '605.f1.b1'], 'core': '55.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5808, 1044, 5722, 4587, 4372, 700, 6330, 2567], 'generators': [55, 110, 6050, 2442], 'label': '66550.bb.55.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '55.b1.b1', 'normal_contained_in': ['5.b1.b1', '11.a1.a1'], 'normal_contains': ['110.c1.b1', '275.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '55.b1.b1', 'projective_image': '66550.bb', 'quotient_action_image': '11.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '55.b1.b1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167042
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['1210.b1.a1', '1210.d1.a1', '1210.e1.a1', '1210.e1.b1', '1210.e1.d1', '1210.e1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['5.b1.c1', '11.a1.a1'], 'contains': ['110.c1.c1', '275.a1.a1', '605.e1.c1', '605.f1.c1'], 'core': '55.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5808, 1044, 6953, 3418, 4372, 700, 7269, 332], 'generators': [55, 110, 6050, 4862], 'label': '66550.bb.55.b1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '55.b1.c1', 'normal_contained_in': ['5.b1.c1', '11.a1.a1'], 'normal_contains': ['110.c1.c1', '275.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '55.b1.c1', 'projective_image': '66550.bb', 'quotient_action_image': '11.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '55.b1.c1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167043
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['1210.b1.a1', '1210.d1.a1', '1210.e1.b1', '1210.e1.c1', '1210.e1.e1', '1210.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5.b1.d1', '11.a1.a1'], 'contains': ['110.c1.d1', '275.a1.a1', '605.e1.d1', '605.f1.d1'], 'core': '55.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5808, 1044, 4997, 427, 4372, 700, 7901, 1077], 'generators': [55, 110, 6050, 1232], 'label': '66550.bb.55.b1.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '55.b1.d1', 'normal_contained_in': ['5.b1.d1', '11.a1.a1'], 'normal_contains': ['110.c1.d1', '275.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '55.b1.d1', 'projective_image': '66550.bb', 'quotient_action_image': '11.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '55.b1.d1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167044
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['1210.b1.a1', '1210.d1.a1', '1210.e1.c1', '1210.e1.d1', '1210.e1.a1', '1210.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['5.b1.e1', '11.a1.a1'], 'contains': ['110.c1.e1', '275.a1.a1', '605.e1.e1', '605.f1.e1'], 'core': '55.b1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5808, 1044, 7334, 1814, 4372, 700, 7585, 3312], 'generators': [55, 110, 6050, 3652], 'label': '66550.bb.55.b1.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '55.b1.e1', 'normal_contained_in': ['5.b1.e1', '11.a1.a1'], 'normal_contains': ['110.c1.e1', '275.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '55.b1.e1', 'projective_image': '66550.bb', 'quotient_action_image': '11.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '55.b1.e1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167045
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.b1.a1'], 'contains': ['110.a1.a1', '275.b1.a1', '605.a1.a1', '605.c1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4038, -1, 779, -1, 6198, -1, 3787, -1], 'generators': [55, 10, 6050, 13310], 'label': '66550.bb.55.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '55.c1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167046
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.b1.a1', '11.b1.a1'], 'contains': ['110.e1.a1', '275.b1.a1', '605.b1.a1', '605.e1.a1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2212, -1, 2876, -1, 7687, -1, 4503, -1], 'generators': [55, 10, 6050, 22], 'label': '66550.bb.55.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '55.d1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.d1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167047
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.b1.b1', '11.b1.a1'], 'contains': ['110.e1.b1', '275.b1.a1', '605.b1.b1', '605.e1.b1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2212, -1, 345, -1, 7687, -1, 4146, -1], 'generators': [55, 10, 6050, 2442], 'label': '66550.bb.55.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '55.d1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.d1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167048
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['13310.b1.a1', '13310.b1.d1', '13310.b1.b1', '13310.b1.e1', '13310.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '25.a1.a1', '55.a1.a1', '55.c1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6162, 7035, 6452, 8147, 2308, 7819, 3337, 7105], 'generators': [55, 10, 110, 13310, 6050], 'label': '66550.bb.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '25.a1.a1', '55.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167049
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.b1.c1', '11.b1.a1'], 'contains': ['110.e1.c1', '275.b1.a1', '605.b1.c1', '605.e1.c1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2212, -1, 1818, -1, 7687, -1, 4861, -1], 'generators': [55, 10, 6050, 4862], 'label': '66550.bb.55.d1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '55.d1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.d1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167050
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.b1.d1', '11.b1.a1'], 'contains': ['110.e1.d1', '275.b1.a1', '605.b1.d1', '605.e1.d1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2212, -1, 1212, -1, 7687, -1, 5575, -1], 'generators': [55, 10, 6050, 1232], 'label': '66550.bb.55.d1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '55.d1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.d1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167051
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '55.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.b1.e1', '11.b1.a1'], 'contains': ['110.e1.e1', '275.b1.a1', '605.b1.e1', '605.e1.e1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2212, -1, 2249, -1, 7687, -1, 5218, -1], 'generators': [55, 10, 6050, 3652], 'label': '66550.bb.55.d1.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '55.d1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.d1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167052
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.a1.a1', 'complements': ['605.f1.a1', '605.f1.d1', '605.f1.b1', '605.f1.e1', '605.f1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.b1.a1', '55.c1.a1'], 'contains': ['550.a1.a1', '1210.a1.a1', '1210.b1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3090, 8956, 4185, 9573, 6310, 8759, 707, 8273], 'generators': [13310, 6050, 10], 'label': '66550.bb.110.a1.a1', 'mobius_quo': 0, 'mobius_sub': -11, 'normal_closure': '110.a1.a1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['550.a1.a1', '1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '110.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167053
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.b1.a1', 'complements': ['605.b1.a1', '605.b1.d1', '605.b1.b1', '605.b1.e1', '605.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.a1', '55.a1.a1'], 'contains': ['550.b1.a1', '1210.a1.a1', '1210.c1.a1'], 'core': '110.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7390, 6291, 9306, 7785, 1355, 6972, 3522, 6989], 'generators': [13310, 6050, 110], 'label': '66550.bb.110.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '110.b1.a1', 'normal_contained_in': ['10.a1.a1', '22.a1.a1', '55.a1.a1'], 'normal_contains': ['550.b1.a1', '1210.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.b1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '110.6', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '110.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.6'}
-
id: 242167054
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['605.a1.a1', '605.b1.d1', '605.b1.e1', '605.b1.b1', '605.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '22.a1.a1', '55.b1.a1'], 'contains': ['550.b1.a1', '1210.f1.a1', '1210.g1.a1'], 'core': '110.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 1044, 8844, 6622, 2481, 2609, 4099, 5003], 'generators': [22, 6050, 110], 'label': '66550.bb.110.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '110.c1.a1', 'normal_contained_in': ['10.b1.a1', '22.a1.a1', '55.b1.a1'], 'normal_contains': ['550.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.c1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '22.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '110.c1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167055
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['605.a1.a1', '605.b1.e1', '605.b1.a1', '605.b1.c1', '605.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '22.a1.a1', '55.b1.b1'], 'contains': ['550.b1.a1', '1210.f1.b1', '1210.g1.b1'], 'core': '110.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 1044, 6686, 4587, 2481, 2609, 3834, 5628], 'generators': [2442, 6050, 110], 'label': '66550.bb.110.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '110.c1.b1', 'normal_contained_in': ['10.b1.b1', '22.a1.a1', '55.b1.b1'], 'normal_contains': ['550.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.c1.b1', 'projective_image': '66550.bb', 'quotient_action_image': '22.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '110.c1.b1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167056
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['605.a1.a1', '605.b1.a1', '605.b1.b1', '605.b1.d1', '605.b1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['10.b1.c1', '22.a1.a1', '55.b1.c1'], 'contains': ['550.b1.a1', '1210.f1.c1', '1210.g1.c1'], 'core': '110.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 1044, 7612, 3034, 2481, 2609, 4363, 3754], 'generators': [4862, 6050, 110], 'label': '66550.bb.110.c1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '110.c1.c1', 'normal_contained_in': ['10.b1.c1', '22.a1.a1', '55.b1.c1'], 'normal_contains': ['550.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.c1.c1', 'projective_image': '66550.bb', 'quotient_action_image': '22.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '110.c1.c1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167057
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['605.a1.a1', '605.b1.b1', '605.b1.c1', '605.b1.e1', '605.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['10.b1.d1', '22.a1.a1', '55.b1.d1'], 'contains': ['550.b1.a1', '1210.f1.d1', '1210.g1.d1'], 'core': '110.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 1044, 5674, 610, 2481, 2609, 4893, 4379], 'generators': [1232, 6050, 110], 'label': '66550.bb.110.c1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '110.c1.d1', 'normal_contained_in': ['10.b1.d1', '22.a1.a1', '55.b1.d1'], 'normal_contains': ['550.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.c1.d1', 'projective_image': '66550.bb', 'quotient_action_image': '22.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '110.c1.d1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167058
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['605.a1.a1', '605.b1.c1', '605.b1.d1', '605.b1.a1', '605.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['10.b1.e1', '22.a1.a1', '55.b1.e1'], 'contains': ['550.b1.a1', '1210.f1.e1', '1210.g1.e1'], 'core': '110.c1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [5324, 1044, 8524, 1912, 2481, 2609, 4628, 6252], 'generators': [3652, 6050, 110], 'label': '66550.bb.110.c1.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '110.c1.e1', 'normal_contained_in': ['10.b1.e1', '22.a1.a1', '55.b1.e1'], 'normal_contains': ['550.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.c1.e1', 'projective_image': '66550.bb', 'quotient_action_image': '22.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '110.c1.e1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167059
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '5.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['13310.a1.a1', '13310.b1.d1', '13310.b1.e1', '13310.b1.b1', '13310.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.a1', '25.a1.a1', '55.b1.a1', '55.d1.a1'], 'core': '5.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2212, 3009, 7972, 6760, 3952, 1265, 4014, 4816], 'generators': [55, 10, 110, 22, 6050], 'label': '66550.bb.5.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.b1.a1', '25.a1.a1', '55.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.b1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
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id: 242167060
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['550.c1.a1', '1210.a1.a1', '1210.d1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1997, -1, 9739, -1, 312, -1, 163, -1], 'generators': [13310, 6050, 120], 'label': '66550.bb.110.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '110.d1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.d1.a1', 'subgroup_fusion': None, 'weyl_group': '11.1'}
-
id: 242167061
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '22.b1.a1', '55.d1.a1'], 'contains': ['550.a1.a1', '1210.e1.a1', '1210.f1.a1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [645, -1, 4828, -1, 7749, -1, 1514, -1], 'generators': [22, 6050, 10], 'label': '66550.bb.110.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '110.e1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.e1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167062
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '22.b1.a1', '55.d1.b1'], 'contains': ['550.a1.a1', '1210.e1.b1', '1210.f1.b1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [645, -1, 3211, -1, 7749, -1, 1097, -1], 'generators': [2442, 6050, 10], 'label': '66550.bb.110.e1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '110.e1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.e1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167063
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.c1', '22.b1.a1', '55.d1.c1'], 'contains': ['550.a1.a1', '1210.e1.c1', '1210.f1.c1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [645, -1, 2707, -1, 7749, -1, 1932, -1], 'generators': [4862, 6050, 10], 'label': '66550.bb.110.e1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '110.e1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.e1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167064
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.d1', '22.b1.a1', '55.d1.d1'], 'contains': ['550.a1.a1', '1210.e1.d1', '1210.f1.d1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [645, -1, 2114, -1, 7749, -1, 2768, -1], 'generators': [1232, 6050, 10], 'label': '66550.bb.110.e1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '110.e1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.e1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167065
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '110.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.e1', '22.b1.a1', '55.d1.e1'], 'contains': ['550.a1.a1', '1210.e1.e1', '1210.f1.e1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [645, -1, 3715, -1, 7749, -1, 2350, -1], 'generators': [3652, 6050, 10], 'label': '66550.bb.110.e1.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '110.e1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.e1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167066
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '121.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.b1.a1'], 'contains': ['242.a1.a1', '605.a1.a1', '605.b1.a1', '605.b1.b1', '605.b1.c1', '605.b1.d1', '605.b1.e1', '1331.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [7581, -1, 867, -1, 8915, -1, 8222, -1], 'generators': [55, 13310, 10, 22], 'label': '66550.bb.121.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '121.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '121.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167067
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '121.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1', '11.b1.a1'], 'contains': ['242.b1.a1', '605.c1.a1', '605.e1.a1', '605.e1.b1', '605.e1.c1', '605.e1.d1', '605.e1.e1', '1331.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5870, -1, 3286, -1, 5557, -1, 6642, -1], 'generators': [55, 13310, 6050, 22], 'label': '66550.bb.121.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '11.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '121.b1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '121.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167068
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '121.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['11.a1.a1'], 'contains': ['242.c1.a1', '605.d1.a1', '605.f1.a1', '605.f1.b1', '605.f1.c1', '605.f1.d1', '605.f1.e1', '1331.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [9380, -1, 5476, -1, 4970, -1, 9205, -1], 'generators': [55, 13310, 110, 22], 'label': '66550.bb.121.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '11.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '121.c1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '121.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167069
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '242.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.b1.a1', '121.a1.a1'], 'contains': ['1210.b1.a1', '1210.e1.a1', '1210.e1.b1', '1210.e1.c1', '1210.e1.d1', '1210.e1.e1', '2662.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [6872, -1, 1032, -1, 9386, -1, 5180, -1], 'generators': [22, 10, 13310], 'label': '66550.bb.242.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167070
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '5.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['13310.a1.a1', '13310.b1.e1', '13310.b1.a1', '13310.b1.c1', '13310.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.b1', '25.a1.a1', '55.b1.b1', '55.d1.b1'], 'core': '5.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2212, 3009, 5988, 5872, 3952, 1265, 3721, 5508], 'generators': [55, 10, 110, 2442, 6050], 'label': '66550.bb.5.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.b1.b1', '25.a1.a1', '55.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '5.b1.b1', 'projective_image': '66550.bb', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.b1.b1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167071
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '242.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '22.b1.a1', '121.b1.a1'], 'contains': ['1210.a1.a1', '1210.f1.a1', '1210.f1.b1', '1210.f1.c1', '1210.f1.d1', '1210.f1.e1', '2662.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4192, -1, 7774, -1, 5296, -1, 3159, -1], 'generators': [22, 6050, 13310], 'label': '66550.bb.242.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '242.b1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167072
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '242.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['22.a1.a1', '121.c1.a1'], 'contains': ['1210.c1.a1', '1210.g1.a1', '1210.g1.b1', '1210.g1.c1', '1210.g1.d1', '1210.g1.e1', '2662.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8823, -1, 7072, -1, 3680, -1, 7292, -1], 'generators': [22, 110, 13310], 'label': '66550.bb.242.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '242.c1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167073
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '275.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['242.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['25.a1.a1', '55.a1.a1', '55.b1.a1', '55.b1.b1', '55.b1.c1', '55.b1.d1', '55.b1.e1'], 'contains': ['550.b1.a1', '3025.b1.a1', '3025.c1.a1'], 'core': '275.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5549, 2335, 6324, 5115, 1963, 4471, 6804, 2844], 'generators': [55, 6050, 110], 'label': '66550.bb.275.a1.a1', 'mobius_quo': 0, 'mobius_sub': -5, 'normal_closure': '275.a1.a1', 'normal_contained_in': ['25.a1.a1', '55.a1.a1', '55.b1.e1', '55.b1.c1', '55.b1.d1', '55.b1.a1', '55.b1.b1'], 'normal_contains': ['550.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '275.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '55.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '275.a1.a1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167074
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '275.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['25.a1.a1', '55.c1.a1', '55.d1.a1', '55.d1.b1', '55.d1.c1', '55.d1.d1', '55.d1.e1'], 'contains': ['550.a1.a1', '3025.a1.a1', '3025.b1.a1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1258, -1, 2039, -1, 7002, -1, 5515, -1], 'generators': [55, 6050, 10], 'label': '66550.bb.275.b1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '25.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '275.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '275.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167075
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '550.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.a1.a1', 'complements': ['121.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['50.a1.a1', '110.a1.a1', '110.e1.a1', '110.e1.b1', '110.e1.c1', '110.e1.d1', '110.e1.e1', '275.b1.a1'], 'contains': ['6050.a1.a1', '6050.b1.a1'], 'core': '550.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [751, 5253, 3991, 9126, 5709, 6342, 2142, 7631], 'generators': [10, 6050], 'label': '66550.bb.550.a1.a1', 'mobius_quo': 0, 'mobius_sub': 55, 'normal_closure': '550.a1.a1', 'normal_contained_in': ['50.a1.a1', '110.a1.a1'], 'normal_contains': ['6050.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '550.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '110.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '550.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167076
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '550.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.b1.a1', 'complements': ['121.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['50.a1.a1', '110.b1.a1', '110.c1.a1', '110.c1.b1', '110.c1.c1', '110.c1.d1', '110.c1.e1', '275.a1.a1'], 'contains': ['6050.a1.a1', '6050.c1.a1'], 'core': '550.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5088, 3625, 8917, 5115, 2250, 5317, 4602, 5628], 'generators': [110, 6050], 'label': '66550.bb.550.b1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '550.b1.a1', 'normal_contained_in': ['50.a1.a1', '110.b1.a1', '110.c1.e1', '110.c1.c1', '110.c1.d1', '110.c1.a1', '110.c1.b1', '275.a1.a1'], 'normal_contains': ['6050.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '550.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '110.6', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '550.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.6'}
-
id: 242167077
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '550.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['50.a1.a1', '110.d1.a1'], 'contains': ['6050.a1.a1', '6050.d1.a1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [219, -1, 9910, -1, 953, -1, 1081, -1], 'generators': [120, 6050], 'label': '66550.bb.550.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '50.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '550.c1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '550.c1.a1', 'subgroup_fusion': None, 'weyl_group': '11.1'}
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id: 242167078
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.c1.a1', '121.a1.a1'], 'contains': ['1210.b1.a1', '3025.a1.a1', '6655.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [6364, -1, 1194, -1, 8915, -1, 7566, -1], 'generators': [55, 10, 13310], 'label': '66550.bb.605.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167079
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.d1.a1', '121.a1.a1'], 'contains': ['1210.e1.a1', '3025.a1.a1', '6655.b1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4015, -1, 2206, -1, 9857, -1, 7933, -1], 'generators': [55, 10, 22], 'label': '66550.bb.605.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167080
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.d1.b1', '121.a1.a1'], 'contains': ['1210.e1.b1', '3025.a1.a1', '6655.b1.b1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4015, -1, 90, -1, 9857, -1, 7749, -1], 'generators': [60555, 10, 2442], 'label': '66550.bb.605.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.b1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167081
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '5.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['13310.a1.a1', '13310.b1.a1', '13310.b1.b1', '13310.b1.d1', '13310.b1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.c1', '25.a1.a1', '55.b1.c1', '55.d1.c1'], 'core': '5.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2212, 3009, 7004, 4760, 3952, 1265, 4307, 3433], 'generators': [55, 10, 110, 4862, 6050], 'label': '66550.bb.5.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.b1.c1', '25.a1.a1', '55.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '5.b1.c1', 'projective_image': '66550.bb', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.b1.c1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167082
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.d1.c1', '121.a1.a1'], 'contains': ['1210.e1.c1', '3025.a1.a1', '6655.b1.c1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4015, -1, 797, -1, 9857, -1, 8116, -1], 'generators': [54505, 10, 4862], 'label': '66550.bb.605.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.b1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167083
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.d1.d1', '121.a1.a1'], 'contains': ['1210.e1.d1', '3025.a1.a1', '6655.b1.d1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4015, -1, 400, -1, 9857, -1, 8483, -1], 'generators': [30305, 10, 1232], 'label': '66550.bb.605.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.b1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.b1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167084
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.d1.e1', '121.a1.a1'], 'contains': ['1210.e1.e1', '3025.a1.a1', '6655.b1.e1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4015, -1, 1504, -1, 9857, -1, 8299, -1], 'generators': [24255, 10, 3652], 'label': '66550.bb.605.b1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '5.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.b1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.b1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167085
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '55.c1.a1', '121.b1.a1'], 'contains': ['1210.a1.a1', '3025.b1.a1', '6655.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5553, -1, 3841, -1, 4648, -1, 5851, -1], 'generators': [55, 6050, 13310], 'label': '66550.bb.605.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '605.c1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167086
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.a1.a1', '121.c1.a1'], 'contains': ['1210.c1.a1', '3025.c1.a1', '6655.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [9781, -1, 5424, -1, 3032, -1, 8731, -1], 'generators': [55, 110, 13310], 'label': '66550.bb.605.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '605.d1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.d1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167087
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1', '55.d1.a1', '121.b1.a1'], 'contains': ['1210.f1.a1', '3025.b1.a1', '6655.b1.a1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3022, -1, 7143, -1, 5807, -1, 6254, -1], 'generators': [55, 6050, 22], 'label': '66550.bb.605.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '55.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '605.e1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.e1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167088
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.b1', '55.d1.b1', '121.b1.a1'], 'contains': ['1210.f1.b1', '3025.b1.a1', '6655.b1.b1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3022, -1, 2982, -1, 5807, -1, 6089, -1], 'generators': [55, 6050, 2442], 'label': '66550.bb.605.e1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '55.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '605.e1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.e1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167089
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.c1', '55.d1.c1', '121.b1.a1'], 'contains': ['1210.f1.c1', '3025.b1.a1', '6655.b1.c1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3022, -1, 4215, -1, 5807, -1, 6418, -1], 'generators': [55, 6050, 4862], 'label': '66550.bb.605.e1.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '55.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '605.e1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.e1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167090
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.d1', '55.d1.d1', '121.b1.a1'], 'contains': ['1210.f1.d1', '3025.b1.a1', '6655.b1.d1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3022, -1, 3180, -1, 5807, -1, 7025, -1], 'generators': [55, 6050, 1232], 'label': '66550.bb.605.e1.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '55.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '605.e1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.e1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167091
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.e1', '55.d1.e1', '121.b1.a1'], 'contains': ['1210.f1.e1', '3025.b1.a1', '6655.b1.e1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3022, -1, 4962, -1, 5807, -1, 6583, -1], 'generators': [55, 6050, 3652], 'label': '66550.bb.605.e1.e1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '55.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '605.e1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.e1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167092
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '5.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['13310.a1.a1', '13310.b1.b1', '13310.b1.c1', '13310.b1.e1', '13310.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.d1', '25.a1.a1', '55.b1.d1', '55.d1.d1'], 'core': '5.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2212, 3009, 3390, 2267, 3952, 1265, 4893, 4124], 'generators': [55, 10, 110, 1232, 6050], 'label': '66550.bb.5.b1.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.b1.d1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.b1.d1', '25.a1.a1', '55.b1.d1'], 'normalizer': '1.a1.a1', 'old_label': '5.b1.d1', 'projective_image': '66550.bb', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.b1.d1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167093
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.a1', '121.c1.a1'], 'contains': ['1210.g1.a1', '3025.c1.a1', '6655.b1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8631, -1, 7430, -1, 4191, -1, 9441, -1], 'generators': [55, 110, 22], 'label': '66550.bb.605.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '605.f1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.f1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167094
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.b1', '121.c1.a1'], 'contains': ['1210.g1.b1', '3025.c1.a1', '6655.b1.b1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8631, -1, 4675, -1, 4191, -1, 8969, -1], 'generators': [60555, 110, 2442], 'label': '66550.bb.605.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '605.f1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.f1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167095
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.c1', '121.c1.a1'], 'contains': ['1210.g1.c1', '3025.c1.a1', '6655.b1.c1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8631, -1, 5711, -1, 4191, -1, 9606, -1], 'generators': [54505, 110, 4862], 'label': '66550.bb.605.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '605.f1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.f1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167096
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.d1', '121.c1.a1'], 'contains': ['1210.g1.d1', '3025.c1.a1', '6655.b1.d1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8631, -1, 3554, -1, 4191, -1, 9935, -1], 'generators': [30305, 110, 1232], 'label': '66550.bb.605.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '605.f1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.f1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167097
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '605.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['55.b1.e1', '121.c1.a1'], 'contains': ['1210.g1.e1', '3025.c1.a1', '6655.b1.e1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8631, -1, 6258, -1, 4191, -1, 9770, -1], 'generators': [24255, 110, 3652], 'label': '66550.bb.605.f1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '55.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '605.f1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.f1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167098
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['110.a1.a1', '110.b1.a1', '110.d1.a1', '242.b1.a1', '605.c1.a1'], 'contains': ['6050.a1.a1', '13310.a1.a1'], 'core': '1210.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4887, 6276, 8917, 9092, 4597, 7273, 3514, 8073], 'generators': [13310, 6050], 'label': '66550.bb.1210.a1.a1', 'mobius_quo': 1, 'mobius_sub': 11, 'normal_closure': '1210.a1.a1', 'normal_contained_in': ['110.a1.a1', '110.b1.a1'], 'normal_contains': ['6050.a1.a1', '13310.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1210.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '10.2', 'quotient_action_kernel': '121.2', 'quotient_action_kernel_order': 121, 'quotient_fusion': None, 'short_label': '1210.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 242167099
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '11.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.a1.a1', '242.a1.a1', '605.a1.a1'], 'contains': ['6050.b1.a1', '13310.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5573, -1, 2407, -1, 7002, -1, 5014, -1], 'generators': [13310, 10], 'label': '66550.bb.1210.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '1210.b1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167100
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.b1.a1', '242.c1.a1', '605.d1.a1'], 'contains': ['6050.c1.a1', '13310.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9781, -1, 7897, -1, 3264, -1, 6337, -1], 'generators': [13310, 110], 'label': '66550.bb.1210.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '1210.c1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.c1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
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id: 242167101
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '110.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.d1.a1'], 'contains': ['6050.d1.a1', '13310.a1.a1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 110, 'diagramx': [1991, -1, 9604, -1, 1775, -1, 894, -1], 'generators': [13310, 120], 'label': '66550.bb.1210.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '110.d1.a1', 'old_label': '1210.d1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167102
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.a1', '242.a1.a1', '605.b1.a1'], 'contains': ['6050.b1.a1', '13310.b1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3871, -1, 2206, -1, 7749, -1, 5346, -1], 'generators': [22, 10], 'label': '66550.bb.1210.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.e1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167103
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '5.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': ['13310.a1.a1', '13310.b1.c1', '13310.b1.d1', '13310.b1.a1', '13310.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.e1', '25.a1.a1', '55.b1.e1', '55.d1.e1'], 'core': '5.b1.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [2212, 3009, 7357, 3390, 3952, 1265, 4600, 6199], 'generators': [55, 10, 110, 3652, 6050], 'label': '66550.bb.5.b1.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.b1.e1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.b1.e1', '25.a1.a1', '55.b1.e1'], 'normalizer': '1.a1.a1', 'old_label': '5.b1.e1', 'projective_image': '66550.bb', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.b1.e1', 'subgroup_fusion': None, 'weyl_group': '13310.bf'}
-
id: 242167104
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.b1', '242.a1.a1', '605.b1.b1'], 'contains': ['6050.b1.a1', '13310.b1.b1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3871, -1, 478, -1, 7749, -1, 5180, -1], 'generators': [2442, 10], 'label': '66550.bb.1210.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.e1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167105
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.c1', '242.a1.a1', '605.b1.c1'], 'contains': ['6050.b1.a1', '13310.b1.c1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3871, -1, 1198, -1, 7749, -1, 5513, -1], 'generators': [4862, 10], 'label': '66550.bb.1210.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.e1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167106
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.d1', '242.a1.a1', '605.b1.d1'], 'contains': ['6050.b1.a1', '13310.b1.d1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3871, -1, 188, -1, 7749, -1, 5846, -1], 'generators': [1232, 10], 'label': '66550.bb.1210.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.e1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.e1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167107
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.e1.e1', '242.a1.a1', '605.b1.e1'], 'contains': ['6050.b1.a1', '13310.b1.e1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3871, -1, 1833, -1, 7749, -1, 5679, -1], 'generators': [3652, 10], 'label': '66550.bb.1210.e1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.e1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.e1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 242167108
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1', '110.e1.a1', '242.b1.a1', '605.e1.a1'], 'contains': ['6050.a1.a1', '13310.b1.a1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2706, -1, 8581, -1, 5296, -1, 3936, -1], 'generators': [22, 6050], 'label': '66550.bb.1210.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '110.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '1210.f1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.f1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167109
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.b1', '110.e1.b1', '242.b1.a1', '605.e1.b1'], 'contains': ['6050.a1.a1', '13310.b1.b1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2706, -1, 5788, -1, 5296, -1, 3711, -1], 'generators': [2442, 6050], 'label': '66550.bb.1210.f1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '110.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '1210.f1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.f1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167110
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.c1', '110.e1.c1', '242.b1.a1', '605.e1.c1'], 'contains': ['6050.a1.a1', '13310.b1.c1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2706, -1, 6681, -1, 5296, -1, 4161, -1], 'generators': [4862, 6050], 'label': '66550.bb.1210.f1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '110.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '1210.f1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.f1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167111
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.d1', '110.e1.d1', '242.b1.a1', '605.e1.d1'], 'contains': ['6050.a1.a1', '13310.b1.d1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2706, -1, 4375, -1, 5296, -1, 4817, -1], 'generators': [1232, 6050], 'label': '66550.bb.1210.f1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '110.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '1210.f1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.f1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167112
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.e1', '110.e1.e1', '242.b1.a1', '605.e1.e1'], 'contains': ['6050.a1.a1', '13310.b1.e1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2706, -1, 8221, -1, 5296, -1, 4386, -1], 'generators': [3652, 6050], 'label': '66550.bb.1210.f1.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '110.c1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '1210.f1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.f1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167113
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.a1', '242.c1.a1', '605.f1.a1'], 'contains': ['6050.c1.a1', '13310.b1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8191, -1, 7660, -1, 3963, -1, 6759, -1], 'generators': [22, 110], 'label': '66550.bb.1210.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '1210.g1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.g1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 242167114
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.a1.a1', 'complements': ['6655.b1.a1', '6655.b1.d1', '6655.b1.b1', '6655.b1.e1', '6655.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['50.a1.a1', '110.a1.a1', '110.b1.a1', '110.d1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3272, 8885, 9083, 8880, 1163, 9050, 913, 9549], 'generators': [13310, 110, 6050, 10], 'label': '66550.bb.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['50.a1.a1', '110.a1.a1', '110.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1210.8'}
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id: 242167115
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.b1', '242.c1.a1', '605.f1.b1'], 'contains': ['6050.c1.a1', '13310.b1.b1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8191, -1, 4822, -1, 3963, -1, 6534, -1], 'generators': [2442, 110], 'label': '66550.bb.1210.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '1210.g1.b1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.g1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 242167116
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.c1', '242.c1.a1', '605.f1.c1'], 'contains': ['6050.c1.a1', '13310.b1.c1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8191, -1, 6321, -1, 3963, -1, 6984, -1], 'generators': [4862, 110], 'label': '66550.bb.1210.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '1210.g1.c1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.g1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 242167117
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.d1', '242.c1.a1', '605.f1.d1'], 'contains': ['6050.c1.a1', '13310.b1.d1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8191, -1, 3754, -1, 3963, -1, 7434, -1], 'generators': [1232, 110], 'label': '66550.bb.1210.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '1210.g1.d1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.g1.d1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 242167118
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1210.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['110.c1.e1', '242.c1.a1', '605.f1.e1'], 'contains': ['6050.c1.a1', '13310.b1.e1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8191, -1, 7389, -1, 3963, -1, 7209, -1], 'generators': [3652, 110], 'label': '66550.bb.1210.g1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.c1.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '1210.g1.e1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.g1.e1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 242167119
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '1331.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['121.a1.a1', '121.b1.a1', '121.c1.a1'], 'contains': ['2662.a1.a1', '6655.a1.a1', '6655.b1.a1', '6655.b1.b1', '6655.b1.c1', '6655.b1.d1', '6655.b1.e1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [7721, -1, 3531, -1, 8444, -1, 9205, -1], 'generators': [55, 13310, 22], 'label': '66550.bb.1331.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '11.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1331.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1331.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167120
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '2662.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['242.a1.a1', '242.b1.a1', '242.c1.a1', '1331.a1.a1'], 'contains': ['13310.a1.a1', '13310.b1.a1', '13310.b1.b1', '13310.b1.c1', '13310.b1.d1', '13310.b1.e1'], 'core': '13310.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [6853, -1, 6369, -1, 6376, -1, 6006, -1], 'generators': [22, 13310], 'label': '66550.bb.2662.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '22.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '2662.a1.a1', 'projective_image': '13310.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2662.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167121
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '3025.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['275.b1.a1', '605.a1.a1', '605.b1.a1', '605.b1.b1', '605.b1.c1', '605.b1.d1', '605.b1.e1'], 'contains': ['6050.b1.a1', '33275.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4355, -1, 1283, -1, 7321, -1, 7630, -1], 'generators': [55, 10], 'label': '66550.bb.3025.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '25.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '3025.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3025.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 242167122
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '3025.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1210.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['275.a1.a1', '275.b1.a1', '605.c1.a1', '605.e1.a1', '605.e1.b1', '605.e1.c1', '605.e1.d1', '605.e1.e1'], 'contains': ['6050.a1.a1', '33275.a1.a1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3324, -1, 4625, -1, 4919, -1, 6169, -1], 'generators': [55, 6050], 'label': '66550.bb.3025.b1.a1', 'mobius_quo': None, 'mobius_sub': 5, 'normal_closure': '275.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.b1.a1', 'old_label': '3025.b1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3025.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 242167123
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '3025.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13310.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['275.a1.a1', '605.d1.a1', '605.f1.a1', '605.f1.b1', '605.f1.c1', '605.f1.d1', '605.f1.e1'], 'contains': ['6050.c1.a1', '33275.a1.a1'], 'core': '66550.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [9144, -1, 5651, -1, 3586, -1, 8969, -1], 'generators': [55, 110], 'label': '66550.bb.3025.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '275.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.c1.a1', 'old_label': '3025.c1.a1', 'projective_image': '66550.bb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3025.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 242167124
{'ambient': '66550.bb', 'aut_centralizer_order': None, 'aut_label': '6050.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '10.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['550.a1.a1', '550.b1.a1', '550.c1.a1', '1210.a1.a1', '1210.f1.a1', '1210.f1.b1', '1210.f1.c1', '1210.f1.d1', '1210.f1.e1', '3025.b1.a1'], 'contains': ['66550.a1.a1'], 'core': '6050.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2778, 5308, 8244, 8731, 4919, 6427, 4161, 7671], 'generators': [6050], 'label': '66550.bb.6050.a1.a1', 'mobius_quo': -1, 'mobius_sub': -55, 'normal_closure': '6050.a1.a1', 'normal_contained_in': ['550.a1.a1', '550.b1.a1', '1210.a1.a1'], 'normal_contains': ['66550.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6050.a1.a1', 'projective_image': '66550.bb', 'quotient_action_image': '10.2', 'quotient_action_kernel': '605.7', 'quotient_action_kernel_order': 605, 'quotient_fusion': None, 'short_label': '6050.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
