-
label: 1T1
{'ab': 1, 'abstract_label': '1.1', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[1,1]', 'gens': [], 'label': '1T1', 'n': 1, 'name': 'Trivial group', 'nilpotency': 0, 'num_conj_classes': 1, 'order': 1, 'parity': 1, 'pretty': 'Trivial', 'prim': 1, 'quotients': [], 'siblings': [], 'solv': 1, 'subfields': [], 't': 1}
-
label: 2T1
{'ab': 1, 'abstract_label': '2.1', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[2,1]', 'gens': [[[1, 2]]], 'isomorphism': [1], 'label': '2T1', 'moddecompuniq': [0], 'n': 2, 'name': 'S2', 'nilpotency': 1, 'num_conj_classes': 2, 'order': 2, 'parity': -1, 'pretty': '$C_2$', 'prim': 1, 'quotients': [], 'siblings': [], 'solv': 1, 'subfields': [], 't': 1}
-
label: 3T1
{'ab': 1, 'abstract_label': '3.1', 'arith_equiv': 0, 'aut_label': '3.1', 'auts': 3, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[3,1]', 'gens': [[[1, 2, 3]]], 'isomorphism': [3], 'label': '3T1', 'moddecompuniq': [0], 'n': 3, 'name': 'A3', 'nilpotency': 1, 'num_conj_classes': 3, 'order': 3, 'parity': 1, 'pretty': '$C_3$', 'prim': 1, 'quotients': [], 'siblings': [], 'solv': 1, 'subfields': [], 't': 1}
-
label: 3T2
{'ab': 0, 'abstract_label': '6.1', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1, 'gapidfull': '[6,1]', 'gens': [[[1, 3]], [[1, 2]]], 'isomorphism': [1, 4], 'label': '3T2', 'moddecompuniq': [1, [[[1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0]], [[0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0]], [[1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0]]]], 'n': 3, 'name': 'S3', 'nilpotency': -1, 'num_conj_classes': 3, 'order': 6, 'parity': -1, 'pretty': '$S_3$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[6, 2], 1]], 'solv': 1, 'subfields': [], 't': 2}
-
label: 4T1
{'ab': 1, 'abstract_label': '4.1', 'arith_equiv': 0, 'aut_label': '4.1', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[4,1]', 'gens': [[[1, 2, 3, 4]]], 'isomorphism': [9], 'label': '4T1', 'moddecompuniq': [0], 'n': 4, 'name': 'C(4) = 4', 'nilpotency': 1, 'num_conj_classes': 4, 'order': 4, 'parity': -1, 'pretty': '$C_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1]], 'siblings': [], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 1}
-
label: 4T2
{'ab': 1, 'abstract_label': '4.2', 'arith_equiv': 0, 'aut_label': '4.2', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 2, 'gapidfull': '[4,2]', 'gens': [[[1, 2], [3, 4]], [[1, 4], [2, 3]]], 'isomorphism': [23, 7], 'label': '4T2', 'moddecompuniq': [0], 'n': 4, 'name': 'E(4) = 2[x]2', 'nilpotency': 1, 'num_conj_classes': 4, 'order': 4, 'parity': 1, 'pretty': '$C_2^2$', 'prim': 0, 'quotients': [[2, [2, 1], 3]], 'siblings': [], 'solv': 1, 'subfields': [[[2, 1], 3]], 't': 2}
-
label: 4T3
{'ab': 0, 'abstract_label': '8.3', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[8,3]', 'gens': [[[1, 2, 3, 4]], [[1, 3]]], 'isomorphism': [5, 9], 'label': '4T3', 'n': 4, 'name': 'D(4)', 'nilpotency': 2, 'num_conj_classes': 5, 'order': 8, 'parity': -1, 'pretty': '$D_{4}$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1]], 'siblings': [[[4, 3], 1], [[8, 4], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 3}
-
label: 4T4
{'ab': 0, 'abstract_label': '12.3', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[12,3]', 'gens': [[[2, 3, 4]], [[1, 3, 4]]], 'isomorphism': [4, 16, 7], 'label': '4T4', 'n': 4, 'name': 'A4', 'nilpotency': -1, 'num_conj_classes': 4, 'order': 12, 'parity': 1, 'pretty': '$A_4$', 'prim': 1, 'quotients': [[3, [3, 1], 1]], 'siblings': [[[6, 4], 1], [[12, 4], 1]], 'solv': 1, 'subfields': [], 't': 4}
-
label: 4T5
{'ab': 0, 'abstract_label': '24.12', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 12, 'gapidfull': '[24,12]', 'gens': [[[1, 2, 3, 4]], [[1, 2]]], 'isomorphism': [2, 4, 16, 7], 'label': '4T5', 'n': 4, 'name': 'S4', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 24, 'parity': -1, 'pretty': '$S_4$', 'prim': 1, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1]], 'siblings': [[[6, 7], 1], [[6, 8], 1], [[8, 14], 1], [[12, 8], 1], [[12, 9], 1], [[24, 10], 1]], 'solv': 1, 'subfields': [], 't': 5}
-
label: 5T1
{'ab': 1, 'abstract_label': '5.1', 'arith_equiv': 0, 'aut_label': '5.1', 'auts': 5, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[5,1]', 'gens': [[[1, 2, 3, 4, 5]]], 'isomorphism': [33], 'label': '5T1', 'moddecompuniq': [0], 'n': 5, 'name': 'C(5) = 5', 'nilpotency': 1, 'num_conj_classes': 5, 'order': 5, 'parity': 1, 'pretty': '$C_5$', 'prim': 1, 'quotients': [], 'siblings': [], 'solv': 1, 'subfields': [], 't': 1}
-
label: 5T2
{'ab': 0, 'abstract_label': '10.1', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1, 'gapidfull': '[10,1]', 'gens': [[[1, 2, 3, 4, 5]], [[1, 4], [2, 3]]], 'isomorphism': [23, 33], 'label': '5T2', 'moddecompuniq': [1, [[[1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0]], [[0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0]], [[1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0]]]], 'n': 5, 'name': 'D(5) = 5:2', 'nilpotency': -1, 'num_conj_classes': 4, 'order': 10, 'parity': 1, 'pretty': '$D_{5}$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[10, 2], 1]], 'solv': 1, 'subfields': [], 't': 2}
-
label: 5T3
{'ab': 0, 'abstract_label': '20.3', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[20,3]', 'gens': [[[1, 2, 3, 4, 5]], [[1, 2, 4, 3]]], 'isomorphism': [13, 33], 'label': '5T3', 'n': 5, 'name': 'F(5) = 5:4', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 20, 'parity': -1, 'pretty': '$F_5$', 'prim': 1, 'quotients': [[2, [2, 1], 1], [4, [4, 1], 1]], 'siblings': [[[10, 4], 1], [[20, 5], 1]], 'solv': 1, 'subfields': [], 't': 3}
-
label: 5T4
{'ab': 0, 'abstract_label': '60.5', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 5, 'gapidfull': '[60,5]', 'gens': [[[1, 2, 3]], [[3, 4, 5]]], 'isomorphism': [33, 30], 'label': '5T4', 'n': 5, 'name': 'A5', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 60, 'parity': 1, 'pretty': '$A_5$', 'prim': 1, 'quotients': [], 'siblings': [[[6, 12], 1], [[10, 7], 1], [[12, 33], 1], [[15, 5], 1], [[20, 15], 1], [[30, 9], 1]], 'solv': 0, 'subfields': [], 't': 4}
-
label: 5T5
{'ab': 0, 'abstract_label': '120.34', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 34, 'gapidfull': '[120,34]', 'gens': [[[1, 2]], [[1, 2, 3, 4, 5]]], 'isomorphism': [24, 33], 'label': '5T5', 'n': 5, 'name': 'S5', 'nilpotency': -1, 'num_conj_classes': 7, 'order': 120, 'parity': -1, 'pretty': '$S_5$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[6, 14], 1], [[10, 12], 1], [[10, 13], 1], [[12, 74], 1], [[15, 10], 1], [[20, 30], 1], [[20, 32], 1], [[20, 35], 1], [[24, 202], 1], [[30, 22], 1], [[30, 25], 1], [[30, 27], 1], [[40, 62], 1]], 'solv': 0, 'subfields': [], 't': 5}
-
label: 6T1
{'ab': 1, 'abstract_label': '6.2', 'arith_equiv': 0, 'aut_label': '6.2', 'auts': 6, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 2, 'gapidfull': '[6,2]', 'gens': [[[1, 2, 3, 4, 5, 6]]], 'isomorphism': [153], 'label': '6T1', 'n': 6, 'name': 'C(6) = 6 = 3[x]2', 'nilpotency': 1, 'num_conj_classes': 6, 'order': 6, 'parity': -1, 'pretty': '$C_6$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1]], 'siblings': [], 'solv': 1, 'subfields': [[[2, 1], 1], [[3, 1], 1]], 't': 1}
-
label: 6T2
{'ab': 0, 'abstract_label': '6.1', 'arith_equiv': 0, 'aut_label': '6.1', 'auts': 6, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1, 'gapidfull': '[6,1]', 'gens': [[[1, 3, 5], [2, 4, 6]], [[1, 4], [2, 3], [5, 6]]], 'isomorphism': [415, 576], 'label': '6T2', 'moddecompuniq': [1, [[[1, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0]], [[0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0, 0]], [[1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 1, 0]]]], 'n': 6, 'name': 'D_6(6) = [3]2', 'nilpotency': -1, 'num_conj_classes': 3, 'order': 6, 'parity': -1, 'pretty': '$S_3$', 'prim': 0, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[3, 2], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[3, 2], 1]], 't': 2}
-
label: 6T3
{'ab': 0, 'abstract_label': '12.4', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 4, 'gapidfull': '[12,4]', 'gens': [[[1, 4], [2, 3], [5, 6]], [[1, 2, 3, 4, 5, 6]]], 'isomorphism': [415, 600], 'label': '6T3', 'n': 6, 'name': 'D(6) = S(3)[x]2', 'nilpotency': -1, 'num_conj_classes': 6, 'order': 12, 'parity': -1, 'pretty': '$D_{6}$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 1]], 'siblings': [[[6, 3], 1], [[12, 3], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[3, 2], 1]], 't': 3}
-
label: 6T4
{'ab': 0, 'abstract_label': '12.3', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[12,3]', 'gens': [[[1, 4], [2, 5]], [[1, 3, 5], [2, 4, 6]]], 'isomorphism': [304, 444, 403], 'label': '6T4', 'n': 6, 'name': 'A_4(6) = [2^2]3', 'nilpotency': -1, 'num_conj_classes': 4, 'order': 12, 'parity': 1, 'pretty': '$A_4$', 'prim': 0, 'quotients': [[3, [3, 1], 1]], 'siblings': [[[4, 4], 1], [[12, 4], 1]], 'solv': 1, 'subfields': [[[3, 1], 1]], 't': 4}
-
label: 6T5
{'ab': 0, 'abstract_label': '18.3', 'arith_equiv': 0, 'aut_label': '3.1', 'auts': 3, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[18,3]', 'gens': [[[1, 4], [2, 5], [3, 6]], [[2, 4, 6]]], 'isomorphism': [600, 356], 'label': '6T5', 'n': 6, 'name': 'F_18(6) = [3^2]2 = 3 wr 2', 'nilpotency': -1, 'num_conj_classes': 9, 'order': 18, 'parity': -1, 'pretty': '$S_3\\times C_3$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [3, 2], 1], [6, [6, 1], 1]], 'siblings': [[[9, 4], 1], [[18, 3], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 5}
-
label: 6T6
{'ab': 0, 'abstract_label': '24.13', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 13, 'gapidfull': '[24,13]', 'gens': [[[1, 3, 5], [2, 4, 6]], [[3, 6]]], 'isomorphism': [450, 304, 444, 403], 'label': '6T6', 'n': 6, 'name': '2A_4(6) = [2^3]3 = 2 wr 3', 'nilpotency': -1, 'num_conj_classes': 8, 'order': 24, 'parity': -1, 'pretty': '$A_4\\times C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [6, 1], 1], [12, [4, 4], 1]], 'siblings': [[[8, 13], 1], [[12, 6], 1], [[12, 7], 1], [[24, 9], 1]], 'solv': 1, 'subfields': [[[3, 1], 1]], 't': 6}
-
label: 6T7
{'ab': 0, 'abstract_label': '24.12', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 12, 'gapidfull': '[24,12]', 'gens': [[[1, 4], [2, 5]], [[1, 5], [2, 4]], [[1, 3, 5], [2, 4, 6]]], 'isomorphism': [269, 304, 94, 444], 'label': '6T7', 'n': 6, 'name': 'S_4(6d) = [2^2]S(3)', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 24, 'parity': 1, 'pretty': '$S_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1]], 'siblings': [[[4, 5], 1], [[6, 8], 1], [[8, 14], 1], [[12, 8], 1], [[12, 9], 1], [[24, 10], 1]], 'solv': 1, 'subfields': [[[3, 2], 1]], 't': 7}
-
label: 6T8
{'ab': 0, 'abstract_label': '24.12', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 12, 'gapidfull': '[24,12]', 'gens': [[[1, 5], [2, 4], [3, 6]], [[1, 4], [2, 5]], [[1, 3, 5], [2, 4, 6]]], 'isomorphism': [316, 680, 94, 444], 'label': '6T8', 'n': 6, 'name': 'S_4(6c) = 1/2[2^3]S(3)', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 24, 'parity': -1, 'pretty': '$S_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1]], 'siblings': [[[4, 5], 1], [[6, 7], 1], [[8, 14], 1], [[12, 8], 1], [[12, 9], 1], [[24, 10], 1]], 'solv': 1, 'subfields': [[[3, 2], 1]], 't': 8}
-
label: 6T9
{'ab': 0, 'abstract_label': '36.10', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 10, 'gapidfull': '[36,10]', 'gens': [[[1, 4], [2, 5], [3, 6]], [[2, 4, 6]], [[1, 5], [2, 4]]], 'isomorphism': [450, 143, 304, 356], 'label': '6T9', 'n': 6, 'name': 'F_18(6):2 = [1/2.S(3)^2]2', 'nilpotency': -1, 'num_conj_classes': 9, 'order': 36, 'parity': -1, 'pretty': '$S_3^2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 2], [12, [6, 3], 2]], 'siblings': [[[9, 8], 1], [[12, 16], 1], [[18, 9], 1], [[18, 11], 2], [[36, 13], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 9}
-
label: 6T10
{'ab': 0, 'abstract_label': '36.9', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 9, 'gapidfull': '[36,9]', 'gens': [[[1, 4, 5, 2], [3, 6]], [[2, 4, 6]], [[1, 5], [2, 4]]], 'isomorphism': [382, 566, 576, 278], 'label': '6T10', 'n': 6, 'name': 'F_36(6) = 1/2[S(3)^2]2', 'nilpotency': -1, 'num_conj_classes': 6, 'order': 36, 'parity': 1, 'pretty': '$C_3^2:C_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [4, [4, 1], 1]], 'siblings': [[[6, 10], 1], [[9, 9], 1], [[12, 17], 2], [[18, 10], 1], [[36, 14], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 10}
-
label: 6T11
{'ab': 0, 'abstract_label': '48.48', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 48, 'gapidfull': '[48,48]', 'gens': [[[1, 5], [2, 4]], [[1, 3, 5], [2, 4, 6]], [[3, 6]]], 'isomorphism': [566, 450, 304, 403, 94], 'label': '6T11', 'n': 6, 'name': '2S_4(6) = [2^3]S(3) = 2 wr S(3)', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 48, 'parity': -1, 'pretty': '$S_4\\times C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 1], [12, [6, 3], 1], [24, [4, 5], 1]], 'siblings': [[[6, 11], 1], [[8, 24], 2], [[12, 21], 1], [[12, 22], 1], [[12, 23], 2], [[12, 24], 2], [[16, 61], 1], [[24, 46], 1], [[24, 47], 1], [[24, 48], 2]], 'solv': 1, 'subfields': [[[3, 2], 1]], 't': 11}
-
label: 6T12
{'ab': 0, 'abstract_label': '60.5', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 5, 'gapidfull': '[60,5]', 'gens': [[[1, 4], [5, 6]], [[1, 2, 3, 4, 6]]], 'isomorphism': [487, 676], 'label': '6T12', 'n': 6, 'name': 'L(6) = PSL(2,5) = A_5(6)', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 60, 'parity': 1, 'pretty': '$\\PSL(2,5)$', 'prim': 1, 'quotients': [], 'siblings': [[[5, 4], 1], [[10, 7], 1], [[12, 33], 1], [[15, 5], 1], [[20, 15], 1], [[30, 9], 1]], 'solv': 0, 'subfields': [], 't': 12}
-
label: 6T13
{'ab': 0, 'abstract_label': '72.40', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 40, 'gapidfull': '[72,40]', 'gens': [[[2, 4]], [[1, 4], [2, 5], [3, 6]], [[2, 4, 6]]], 'isomorphism': [14, 127, 16, 506, 103], 'label': '6T13', 'n': 6, 'name': 'F_36(6):2 = [S(3)^2]2 = S(3) wr 2', 'nilpotency': -1, 'num_conj_classes': 9, 'order': 72, 'parity': -1, 'pretty': '$C_3^2:D_4$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [8, [4, 3], 1]], 'siblings': [[[6, 13], 1], [[9, 16], 1], [[12, 34], 2], [[12, 35], 2], [[12, 36], 2], [[18, 34], 2], [[18, 36], 1], [[24, 72], 2], [[36, 53], 1], [[36, 54], 2]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 13}
-
label: 6T14
{'ab': 0, 'abstract_label': '120.34', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 34, 'gapidfull': '[120,34]', 'gens': [[[1, 2], [3, 4], [5, 6]], [[1, 2, 3, 4, 6]]], 'isomorphism': [341, 296], 'label': '6T14', 'n': 6, 'name': 'L(6):2 = PGL(2,5) = S_5(6)', 'nilpotency': -1, 'num_conj_classes': 7, 'order': 120, 'parity': -1, 'pretty': '$\\PGL(2,5)$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[5, 5], 1], [[10, 12], 1], [[10, 13], 1], [[12, 74], 1], [[15, 10], 1], [[20, 30], 1], [[20, 32], 1], [[20, 35], 1], [[24, 202], 1], [[30, 22], 1], [[30, 25], 1], [[30, 27], 1], [[40, 62], 1]], 'solv': 0, 'subfields': [], 't': 14}
-
label: 6T15
{'ab': 0, 'abstract_label': '360.118', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 118, 'gapidfull': '[360,118]', 'gens': [[[1, 2, 3]], [[1, 2], [3, 4, 5, 6]]], 'isomorphism': [33, 152], 'label': '6T15', 'n': 6, 'name': 'A6', 'nilpotency': -1, 'num_conj_classes': 7, 'order': 360, 'parity': 1, 'pretty': '$A_6$', 'prim': 1, 'quotients': [], 'siblings': [[[6, 15], 1], [[10, 26], 1], [[15, 20], 2], [[20, 89], 1], [[30, 88], 2], [[36, 555], 1], [[40, 304], 1], [[45, 49], 1]], 'solv': 0, 'subfields': [], 't': 15}
-
label: 6T16
{'ab': 0, 'abstract_label': '720.763', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 763, 'gapidfull': '[720,763]', 'gens': [[[1, 2]], [[1, 2, 3, 4, 5, 6]]], 'isomorphism': [120, 153], 'label': '6T16', 'n': 6, 'name': 'S6', 'nilpotency': -1, 'num_conj_classes': 11, 'order': 720, 'parity': -1, 'pretty': '$S_6$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[6, 16], 1], [[10, 32], 1], [[12, 183], 2], [[15, 28], 2], [[20, 145], 1], [[20, 149], 2], [[30, 164], 2], [[30, 166], 2], [[30, 176], 2], [[36, 1252], 1], [[40, 589], 1], [[40, 592], 2], [[45, 96], 1]], 'solv': 0, 'subfields': [], 't': 16}
-
label: 7T1
{'ab': 1, 'abstract_label': '7.1', 'arith_equiv': 0, 'aut_label': '7.1', 'auts': 7, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[7,1]', 'gens': [[[1, 2, 3, 4, 5, 6, 7]]], 'isomorphism': [873], 'label': '7T1', 'n': 7, 'name': 'C(7) = 7', 'nilpotency': 1, 'num_conj_classes': 7, 'order': 7, 'parity': 1, 'pretty': '$C_7$', 'prim': 1, 'quotients': [], 'siblings': [], 'solv': 1, 'subfields': [], 't': 1}
-
label: 7T2
{'ab': 0, 'abstract_label': '14.1', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1, 'gapidfull': '[14,1]', 'gens': [[[1, 6], [2, 5], [3, 4]], [[1, 2, 3, 4, 5, 6, 7]]], 'isomorphism': [719, 3456], 'label': '7T2', 'n': 7, 'name': 'D(7) = 7:2', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 14, 'parity': -1, 'pretty': '$D_{7}$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[14, 2], 1]], 'solv': 1, 'subfields': [], 't': 2}
-
label: 7T3
{'ab': 0, 'abstract_label': '21.1', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1, 'gapidfull': '[21,1]', 'gens': [[[1, 2, 4], [3, 6, 5]], [[1, 2, 3, 4, 5, 6, 7]]], 'isomorphism': [186, 873], 'label': '7T3', 'n': 7, 'name': 'F_21(7) = 7:3', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 21, 'parity': 1, 'pretty': '$C_7:C_3$', 'prim': 1, 'quotients': [[3, [3, 1], 1]], 'siblings': [[[21, 2], 1]], 'solv': 1, 'subfields': [], 't': 3}
-
label: 7T4
{'ab': 0, 'abstract_label': '42.1', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1, 'gapidfull': '[42,1]', 'gens': [[[1, 3, 2, 6, 4, 5]], [[1, 2, 3, 4, 5, 6, 7]]], 'isomorphism': [533, 3456], 'label': '7T4', 'n': 7, 'name': 'F_42(7) = 7:6', 'nilpotency': -1, 'num_conj_classes': 7, 'order': 42, 'parity': -1, 'pretty': '$F_7$', 'prim': 1, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [6, 1], 1]], 'siblings': [[[14, 4], 1], [[21, 4], 1], [[42, 4], 1]], 'solv': 1, 'subfields': [], 't': 4}
-
label: 7T5
{'ab': 0, 'abstract_label': '168.42', 'arith_equiv': 1, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 42, 'gapidfull': '[168,42]', 'gens': [[[1, 2], [3, 6]], [[1, 2, 3, 4, 5, 6, 7]]], 'isomorphism': [3740, 4838], 'label': '7T5', 'n': 7, 'name': 'L(7) = L(3,2)', 'nilpotency': -1, 'num_conj_classes': 6, 'order': 168, 'parity': 1, 'pretty': '$\\GL(3,2)$', 'prim': 1, 'quotients': [], 'siblings': [[[7, 5], 1], [[8, 37], 1], [[14, 10], 2], [[21, 14], 1], [[24, 284], 1], [[28, 32], 1], [[42, 37], 1], [[42, 38], 2]], 'solv': 0, 'subfields': [], 't': 5}
-
label: 7T6
{'ab': 0, 'abstract_label': '2520.a', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 0, 'gapidfull': '', 'gens': [[[3, 4, 5, 6, 7]], [[1, 2, 3]]], 'isomorphism': [33, 840], 'label': '7T6', 'n': 7, 'name': 'A7', 'nilpotency': -1, 'num_conj_classes': 9, 'order': 2520, 'parity': 1, 'pretty': '$A_7$', 'prim': 1, 'quotients': [], 'siblings': [[[15, 47], 2], [[21, 33], 1], [[35, 28], 1], [[42, 294], 1], [[42, 299], 1]], 'solv': 0, 'subfields': [], 't': 6}
-
label: 7T7
{'ab': 0, 'abstract_label': '5040.w', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 0, 'gapidfull': '', 'gens': [[[1, 2, 3, 4, 5, 6, 7]], [[1, 2]]], 'isomorphism': [873, 720], 'label': '7T7', 'n': 7, 'name': 'S7', 'nilpotency': -1, 'num_conj_classes': 15, 'order': 5040, 'parity': -1, 'pretty': '$S_7$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[14, 46], 1], [[21, 38], 1], [[30, 565], 1], [[35, 31], 1], [[42, 411], 1], [[42, 412], 1], [[42, 413], 1], [[42, 418], 1]], 'solv': 0, 'subfields': [], 't': 7}
-
label: 8T1
{'ab': 1, 'abstract_label': '8.1', 'arith_equiv': 0, 'aut_label': '8.1', 'auts': 8, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[8,1]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]]], 'isomorphism': [5913], 'label': '8T1', 'n': 8, 'name': 'C(8)=8', 'nilpotency': 1, 'num_conj_classes': 8, 'order': 8, 'parity': -1, 'pretty': '$C_8$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [4, [4, 1], 1]], 'siblings': [], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 1], 1]], 't': 1}
-
label: 8T2
{'ab': 1, 'abstract_label': '8.2', 'arith_equiv': 0, 'aut_label': '8.2', 'auts': 8, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 2, 'gapidfull': '[8,2]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [23616, 6425], 'label': '8T2', 'n': 8, 'name': '4[x]2', 'nilpotency': 1, 'num_conj_classes': 8, 'order': 8, 'parity': 1, 'pretty': '$C_4\\times C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1]], 'siblings': [], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 1], 2], [[4, 2], 1]], 't': 2}
-
label: 8T3
{'ab': 1, 'abstract_label': '8.5', 'arith_equiv': 0, 'aut_label': '8.5', 'auts': 8, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 5, 'gapidfull': '[8,5]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [23616, 36899, 14493], 'label': '8T3', 'n': 8, 'name': 'E(8)=2[x]2[x]2', 'nilpotency': 1, 'num_conj_classes': 8, 'order': 8, 'parity': 1, 'pretty': '$C_2^3$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7]], 'siblings': [], 'solv': 1, 'subfields': [[[2, 1], 7], [[4, 2], 7]], 't': 3}
-
label: 8T4
{'ab': 0, 'abstract_label': '8.3', 'arith_equiv': 0, 'aut_label': '8.3', 'auts': 8, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[8,3]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[1, 6], [2, 5], [3, 4], [7, 8]]], 'isomorphism': [28495, 6425], 'label': '8T4', 'n': 8, 'name': 'D_8(8)=[4]2', 'nilpotency': 2, 'num_conj_classes': 5, 'order': 8, 'parity': 1, 'pretty': '$D_4$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1]], 'siblings': [[[4, 3], 2]], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 2], 1], [[4, 3], 2]], 't': 4}
-
label: 8T5
{'ab': 0, 'abstract_label': '8.4', 'arith_equiv': 0, 'aut_label': '8.4', 'auts': 8, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 4, 'gapidfull': '[8,4]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[1, 7, 3, 5], [2, 6, 8, 4]]], 'isomorphism': [34348, 6425], 'label': '8T5', 'n': 8, 'name': 'Q_8(8)', 'nilpotency': 2, 'num_conj_classes': 5, 'order': 8, 'parity': 1, 'pretty': '$Q_8$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1]], 'siblings': [], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 2], 1]], 't': 5}
-
label: 8T6
{'ab': 0, 'abstract_label': '16.7', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 7, 'gapidfull': '[16,7]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[1, 6], [2, 5], [3, 4], [7, 8]]], 'isomorphism': [5039, 5913], 'label': '8T6', 'n': 8, 'name': 'D(8)', 'nilpotency': 3, 'num_conj_classes': 7, 'order': 16, 'parity': -1, 'pretty': '$D_{8}$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [8, [4, 3], 1]], 'siblings': [[[8, 6], 1], [[16, 13], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 6}
-
label: 8T7
{'ab': 0, 'abstract_label': '16.6', 'arith_equiv': 0, 'aut_label': '4.1', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 6, 'gapidfull': '[16,6]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[1, 5], [3, 7]]], 'isomorphism': [3109, 5913], 'label': '8T7', 'n': 8, 'name': '1/2[2^3]4', 'nilpotency': 2, 'num_conj_classes': 10, 'order': 16, 'parity': -1, 'pretty': '$C_8:C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [8, 2], 1]], 'siblings': [[[16, 6], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 1], 1]], 't': 7}
-
label: 8T8
{'ab': 0, 'abstract_label': '16.8', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 8, 'gapidfull': '[16,8]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[1, 3], [2, 6], [5, 7]]], 'isomorphism': [1930, 5913], 'label': '8T8', 'n': 8, 'name': '2D_8(8)=[D(4)]2', 'nilpotency': 3, 'num_conj_classes': 7, 'order': 16, 'parity': -1, 'pretty': '$QD_{16}$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [8, [4, 3], 1]], 'siblings': [[[16, 12], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 8}
-
label: 8T9
{'ab': 0, 'abstract_label': '16.11', 'arith_equiv': 0, 'aut_label': '4.2', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 11, 'gapidfull': '[16,11]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[4, 5], [6, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [23616, 14519, 5759, 36899], 'label': '8T9', 'n': 8, 'name': 'E(8):2=D(4)[x]2', 'nilpotency': 2, 'num_conj_classes': 10, 'order': 16, 'parity': 1, 'pretty': '$D_4\\times C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [4, 3], 2], [8, [8, 3], 1]], 'siblings': [[[8, 9], 3], [[16, 9], 1]], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 2], 1], [[4, 3], 2]], 't': 9}
-
label: 8T10
{'ab': 0, 'abstract_label': '16.3', 'arith_equiv': 0, 'aut_label': '4.2', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[16,3]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[1, 5], [3, 7]]], 'isomorphism': [3109, 23616, 6425], 'label': '8T10', 'n': 8, 'name': '[2^2]4', 'nilpotency': 2, 'num_conj_classes': 10, 'order': 16, 'parity': 1, 'pretty': '$C_2^2:C_4$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1]], 'siblings': [[[8, 10], 1], [[16, 10], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 1], 1], [[4, 3], 2]], 't': 10}
-
label: 8T11
{'ab': 0, 'abstract_label': '16.13', 'arith_equiv': 0, 'aut_label': '4.1', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 13, 'gapidfull': '[16,13]', 'gens': [[[1, 3, 5, 7], [2, 4, 6, 8]], [[1, 5], [3, 7]], [[1, 4, 5, 8], [2, 3, 6, 7]]], 'isomorphism': [19220, 39727, 28783], 'label': '8T11', 'n': 8, 'name': '1/2[2^3]E(4)=Q_8:2', 'nilpotency': 2, 'num_conj_classes': 10, 'order': 16, 'parity': 1, 'pretty': '$Q_8:C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [8, 3], 1]], 'siblings': [[[8, 11], 2], [[16, 11], 1]], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 2], 1]], 't': 11}
-
label: 8T12
{'ab': 0, 'abstract_label': '24.3', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[24,3]', 'gens': [[[1, 3, 5, 7], [2, 4, 6, 8]], [[1, 3, 8], [4, 5, 7]]], 'isomorphism': [11471, 34560], 'label': '8T12', 'n': 8, 'name': '2A_4(8)=[2]A(4)=SL(2,3)', 'nilpotency': -1, 'num_conj_classes': 7, 'order': 24, 'parity': 1, 'pretty': '$\\SL(2,3)$', 'prim': 0, 'quotients': [[3, [3, 1], 1], [12, [4, 4], 1]], 'siblings': [[[24, 7], 1]], 'solv': 1, 'subfields': [[[4, 4], 1]], 't': 12}
-
label: 8T13
{'ab': 0, 'abstract_label': '24.13', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 13, 'gapidfull': '[24,13]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [28495, 5808, 14493, 5759], 'label': '8T13', 'n': 8, 'name': 'E(8):3=A(4)[x]2', 'nilpotency': -1, 'num_conj_classes': 8, 'order': 24, 'parity': 1, 'pretty': '$A_4\\times C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [6, 1], 1], [12, [4, 4], 1]], 'siblings': [[[6, 6], 1], [[12, 6], 1], [[12, 7], 1], [[24, 9], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 4], 1]], 't': 13}
-
label: 8T14
{'ab': 0, 'abstract_label': '24.12', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 12, 'gapidfull': '[24,12]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 2, 3], [5, 6, 7]], [[1, 4], [2, 6], [3, 7], [5, 8]]], 'isomorphism': [28662, 9543, 14493, 36899], 'label': '8T14', 'n': 8, 'name': 'S(4)[1/2]2=1/2(S_4[x]2)', 'nilpotency': -1, 'num_conj_classes': 5, 'order': 24, 'parity': 1, 'pretty': '$S_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1]], 'siblings': [[[4, 5], 1], [[6, 7], 1], [[6, 8], 1], [[12, 8], 1], [[12, 9], 1], [[24, 10], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 5], 1]], 't': 14}
-
label: 8T15
{'ab': 0, 'abstract_label': '32.43', 'arith_equiv': 1, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 43, 'gapidfull': '[32,43]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[1, 5], [3, 7]], [[1, 6], [2, 5], [3, 4], [7, 8]]], 'isomorphism': [3109, 34406, 29400], 'label': '8T15', 'n': 8, 'name': '[1/4.cD(4)^2]2', 'nilpotency': 3, 'num_conj_classes': 11, 'order': 32, 'parity': -1, 'pretty': '$Z_8 : Z_8^\\times$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [4, 3], 2], [8, [8, 3], 1], [16, [8, 9], 1]], 'siblings': [[[8, 15], 1], [[16, 35], 1], [[16, 38], 2], [[16, 45], 1], [[32, 21], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 15}
-
label: 8T16
{'ab': 0, 'abstract_label': '32.7', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 7, 'gapidfull': '[32,7]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[2, 6], [3, 7]]], 'isomorphism': [592, 3109, 5913], 'label': '8T16', 'n': 8, 'name': '1/2[2^4]4', 'nilpotency': 3, 'num_conj_classes': 11, 'order': 32, 'parity': -1, 'pretty': '$(C_8:C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1]], 'siblings': [[[8, 16], 1], [[16, 36], 1], [[16, 41], 2], [[32, 22], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 1], 1]], 't': 16}
-
label: 8T17
{'ab': 0, 'abstract_label': '32.11', 'arith_equiv': 0, 'aut_label': '4.1', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 11, 'gapidfull': '[32,11]', 'gens': [[[1, 2, 3, 8]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [35345, 23616, 32], 'label': '8T17', 'n': 8, 'name': '[4^2]2', 'nilpotency': 3, 'num_conj_classes': 14, 'order': 32, 'parity': -1, 'pretty': '$C_4\\wr C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1]], 'siblings': [[[8, 17], 1], [[16, 28], 1], [[16, 42], 1], [[32, 14], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 17}
-
label: 8T18
{'ab': 0, 'abstract_label': '32.27', 'arith_equiv': 0, 'aut_label': '4.2', 'auts': 4, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 27, 'gapidfull': '[32,27]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[4, 5], [6, 7]], [[4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [26, 60, 19296, 5759, 36899], 'label': '8T18', 'n': 8, 'name': 'E(8):E_4=[2^2]D(4)', 'nilpotency': 2, 'num_conj_classes': 14, 'order': 32, 'parity': 1, 'pretty': '$C_2^2 \\wr C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [4, 3], 6], [8, [8, 3], 1], [16, [8, 9], 3]], 'siblings': [[[8, 18], 7], [[16, 39], 6], [[16, 46], 1], [[32, 24], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 3]], 't': 18}
-
label: 8T19
{'ab': 0, 'abstract_label': '32.6', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 6, 'gapidfull': '[32,6]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]], [[1, 3], [4, 5, 6, 7]]], 'isomorphism': [4545, 36899, 32856], 'label': '8T19', 'n': 8, 'name': 'E(8):4=[1/4.eD(4)^2]2', 'nilpotency': 3, 'num_conj_classes': 11, 'order': 32, 'parity': 1, 'pretty': '$C_2^3 : C_4 $', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1]], 'siblings': [[[8, 19], 1], [[8, 20], 1], [[8, 21], 1], [[16, 33], 2], [[16, 52], 1], [[16, 53], 1], [[32, 19], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 19}
-
label: 8T20
{'ab': 0, 'abstract_label': '32.6', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 6, 'gapidfull': '[32,6]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[2, 6], [3, 7]]], 'isomorphism': [6425, 21410, 14804], 'label': '8T20', 'n': 8, 'name': '[2^3]4', 'nilpotency': 3, 'num_conj_classes': 11, 'order': 32, 'parity': 1, 'pretty': '$C_2^3: C_4$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1]], 'siblings': [[[8, 19], 2], [[8, 21], 1], [[16, 33], 2], [[16, 52], 1], [[16, 53], 1], [[32, 19], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 1], 1]], 't': 20}
-
label: 8T21
{'ab': 0, 'abstract_label': '32.6', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 6, 'gapidfull': '[32,6]', 'gens': [[[1, 4, 5, 8], [2, 3], [6, 7]], [[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 5], [3, 7]]], 'isomorphism': [16727, 3109, 11824], 'label': '8T21', 'n': 8, 'name': '1/2[2^4]E(4)=[1/4.dD(4)^2]2', 'nilpotency': 3, 'num_conj_classes': 11, 'order': 32, 'parity': -1, 'pretty': '$C_2^3: C_4$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1]], 'siblings': [[[8, 19], 2], [[8, 20], 1], [[16, 33], 2], [[16, 52], 1], [[16, 53], 1], [[32, 19], 1]], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 2], 1]], 't': 21}
-
label: 8T22
{'ab': 0, 'abstract_label': '32.49', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 49, 'gapidfull': '[32,49]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[2, 3], [6, 7]], [[2, 3], [4, 5]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [23616, 33538, 36177, 744, 36899], 'label': '8T22', 'n': 8, 'name': 'E(8):D_4=[2^3]2^2', 'nilpotency': 2, 'num_conj_classes': 17, 'order': 32, 'parity': 1, 'pretty': '$Q_8:C_2^2$', 'prim': 0, 'quotients': [[2, [2, 1], 15], [4, [4, 2], 35], [8, [8, 3], 15], [16, [16, 3], 1]], 'siblings': [[[8, 22], 5], [[16, 23], 9], [[32, 9], 1]], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 2], 1]], 't': 22}
-
label: 8T23
{'ab': 0, 'abstract_label': '48.29', 'arith_equiv': 1, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 29, 'gapidfull': '[48,29]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[1, 3, 8], [4, 5, 7]]], 'isomorphism': [39207, 4838], 'label': '8T23', 'n': 8, 'name': '2S_4(8)=GL(2,3)', 'nilpotency': -1, 'num_conj_classes': 8, 'order': 48, 'parity': -1, 'pretty': '$\\textrm{GL(2,3)}$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1], [24, [4, 5], 1]], 'siblings': [[[8, 23], 1], [[16, 66], 1], [[24, 22], 1]], 'solv': 1, 'subfields': [[[4, 5], 1]], 't': 23}
-
label: 8T24
{'ab': 0, 'abstract_label': '48.48', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 48, 'gapidfull': '[48,48]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[2, 3], [4, 5]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [10854, 28495, 5808, 5759, 36899], 'label': '8T24', 'n': 8, 'name': 'E(8):D_6=S(4)[x]2', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 48, 'parity': 1, 'pretty': '$S_4\\times C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 1], [12, [6, 3], 1], [24, [4, 5], 1]], 'siblings': [[[6, 11], 2], [[8, 24], 1], [[12, 21], 1], [[12, 22], 1], [[12, 23], 2], [[12, 24], 2], [[16, 61], 1], [[24, 46], 1], [[24, 47], 1], [[24, 48], 2]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 5], 1]], 't': 24}
-
label: 8T25
{'ab': 0, 'abstract_label': '56.11', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 11, 'gapidfull': '[56,11]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 2, 6, 3, 4, 5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [12000, 23616, 36899, 5759], 'label': '8T25', 'n': 8, 'name': 'E(8):7=F_56(8)', 'nilpotency': -1, 'num_conj_classes': 8, 'order': 56, 'parity': 1, 'pretty': '$C_2^3:C_7$', 'prim': 1, 'quotients': [[7, [7, 1], 1]], 'siblings': [[[14, 6], 1], [[28, 11], 1]], 'solv': 1, 'subfields': [], 't': 25}
-
label: 8T26
{'ab': 0, 'abstract_label': '64.134', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 134, 'gapidfull': '[64,134]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[1, 7], [3, 5], [4, 8]], [[1, 5], [4, 8]]], 'isomorphism': [31426, 5167, 35152, 32483, 3109, 23616], 'label': '8T26', 'n': 8, 'name': '1/2[2^4]eD(4)', 'nilpotency': 3, 'num_conj_classes': 16, 'order': 64, 'parity': -1, 'pretty': '$(C_4^2 : C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [4, 3], 6], [8, [8, 3], 1], [16, [8, 9], 3], [32, [8, 18], 1]], 'siblings': [[[8, 26], 3], [[16, 135], 2], [[16, 141], 2], [[16, 142], 2], [[16, 152], 2], [[32, 147], 2], [[32, 148], 2], [[32, 155], 1], [[32, 156], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 26}
-
label: 8T27
{'ab': 0, 'abstract_label': '64.32', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 32, 'gapidfull': '[64,32]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[4, 8]]], 'isomorphism': [6425, 3030, 3420, 14493, 3109, 23616], 'label': '8T27', 'n': 8, 'name': '[2^4]4', 'nilpotency': 4, 'num_conj_classes': 13, 'order': 64, 'parity': -1, 'pretty': '$((C_8 : C_2):C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1], [32, [8, 19], 1]], 'siblings': [[[8, 27], 1], [[8, 28], 2], [[16, 130], 1], [[16, 157], 2], [[16, 158], 2], [[16, 159], 2], [[16, 166], 1], [[16, 170], 1], [[16, 171], 1], [[16, 172], 1], [[32, 138], 2], [[32, 139], 1], [[32, 170], 1], [[32, 176], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 1], 1]], 't': 27}
-
label: 8T28
{'ab': 0, 'abstract_label': '64.32', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 32, 'gapidfull': '[64,32]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[2, 6], [3, 7]], [[1, 3], [5, 7]]], 'isomorphism': [5247, 10814, 11536, 592, 21410, 23616], 'label': '8T28', 'n': 8, 'name': '1/2[2^4]dD(4)', 'nilpotency': 4, 'num_conj_classes': 13, 'order': 64, 'parity': -1, 'pretty': '$(((C_4 \\times C_2): C_2):C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1], [32, [8, 19], 1]], 'siblings': [[[8, 27], 2], [[8, 28], 1], [[16, 130], 1], [[16, 157], 2], [[16, 158], 2], [[16, 159], 2], [[16, 166], 1], [[16, 170], 1], [[16, 171], 1], [[16, 172], 1], [[32, 138], 2], [[32, 139], 1], [[32, 170], 1], [[32, 176], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 28}
-
label: 8T29
{'ab': 0, 'abstract_label': '64.138', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 138, 'gapidfull': '[64,138]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 5], [2, 6], [3, 7], [4, 8]], [[1, 3], [4, 5, 6, 7]], [[1, 3], [5, 7]]], 'isomorphism': [86, 10814, 23616, 60, 5759, 14493], 'label': '8T29', 'n': 8, 'name': 'E(8):D_8=[2^3]D(4)', 'nilpotency': 3, 'num_conj_classes': 16, 'order': 64, 'parity': 1, 'pretty': '$(((C_4 \\times C_2): C_2):C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [4, 3], 6], [8, [8, 3], 1], [16, [8, 9], 3], [32, [8, 18], 1]], 'siblings': [[[8, 29], 5], [[8, 31], 2], [[16, 127], 1], [[16, 128], 3], [[16, 129], 3], [[16, 147], 1], [[16, 149], 6], [[16, 150], 3], [[32, 136], 3], [[32, 137], 2], [[32, 163], 3]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 29}
-
label: 8T30
{'ab': 0, 'abstract_label': '64.34', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 34, 'gapidfull': '[64,34]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[2, 6], [3, 7]], [[1, 3], [4, 8], [5, 7]]], 'isomorphism': [6425, 32483, 4447], 'label': '8T30', 'n': 8, 'name': '1/2[2^4]cD(4)', 'nilpotency': 4, 'num_conj_classes': 13, 'order': 64, 'parity': -1, 'pretty': '$(((C_4 \\times C_2): C_2):C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 1], 2], [4, [4, 2], 1], [8, [4, 3], 2], [8, [8, 2], 1], [16, [8, 10], 1], [32, [8, 19], 1]], 'siblings': [[[8, 30], 3], [[16, 143], 2], [[16, 167], 2], [[16, 168], 2], [[16, 169], 2], [[32, 157], 2], [[32, 177], 1], [[32, 178], 1]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 30}
-
label: 8T31
{'ab': 0, 'abstract_label': '64.138', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 138, 'gapidfull': '[64,138]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[4, 8]]], 'isomorphism': [512, 14493, 36899, 21410, 3420, 23616], 'label': '8T31', 'n': 8, 'name': '[2^4]E(4)', 'nilpotency': 3, 'num_conj_classes': 16, 'order': 64, 'parity': -1, 'pretty': '$(((C_4 \\times C_2): C_2):C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [4, 3], 6], [8, [8, 3], 1], [16, [8, 9], 3], [32, [8, 18], 1]], 'siblings': [[[8, 29], 6], [[8, 31], 1], [[16, 127], 1], [[16, 128], 3], [[16, 129], 3], [[16, 147], 1], [[16, 149], 6], [[16, 150], 3], [[32, 136], 3], [[32, 137], 2], [[32, 163], 3]], 'solv': 1, 'subfields': [[[2, 1], 3], [[4, 2], 1]], 't': 31}
-
label: 8T32
{'ab': 0, 'abstract_label': '96.204', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 204, 'gapidfull': '[96,204]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[2, 5], [3, 4]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [10110, 13772, 31858, 26190, 2424, 28495], 'label': '8T32', 'n': 8, 'name': '[2^3]A(4)', 'nilpotency': -1, 'num_conj_classes': 11, 'order': 96, 'parity': 1, 'pretty': '$((C_2 \\times D_4): C_2):C_3$', 'prim': 0, 'quotients': [[3, [3, 1], 1], [12, [4, 4], 5], [48, [12, 32], 1]], 'siblings': [[[8, 32], 2], [[24, 97], 3], [[24, 149], 1], [[32, 420], 1]], 'solv': 1, 'subfields': [[[4, 4], 1]], 't': 32}
-
label: 8T33
{'ab': 0, 'abstract_label': '96.70', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 70, 'gapidfull': '[96,70]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [23616, 5768, 60, 86, 14493, 5759], 'label': '8T33', 'n': 8, 'name': 'E(8):A_4=[1/3.A(4)^2]2=E(4):6', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 96, 'parity': 1, 'pretty': '$C_2^4:C_6$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [6, 1], 1], [12, [4, 4], 1], [24, [6, 6], 1]], 'siblings': [[[8, 33], 1], [[12, 58], 2], [[12, 59], 2], [[16, 183], 1], [[24, 181], 2], [[24, 182], 2], [[24, 183], 2], [[24, 184], 2], [[24, 185], 1], [[24, 186], 1], [[32, 389], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 33}
-
label: 8T34
{'ab': 0, 'abstract_label': '96.227', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 227, 'gapidfull': '[96,227]', 'gens': [[[1, 8], [2, 3]], [[1, 2, 3], [5, 6, 7]], [[1, 5], [2, 7], [3, 6], [4, 8]]], 'isomorphism': [24338, 10092, 14459, 36959, 5699, 36933], 'label': '8T34', 'n': 8, 'name': '1/2[E(4)^2:S_3]2=E(4)^2:D_6', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 96, 'parity': 1, 'pretty': '$V_4^2:S_3$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1], [24, [4, 5], 3]], 'siblings': [[[12, 66], 3], [[12, 67], 1], [[12, 68], 3], [[12, 69], 1], [[16, 194], 1], [[24, 195], 3], [[24, 196], 3], [[24, 197], 3], [[24, 198], 1], [[24, 199], 1], [[24, 200], 3], [[32, 398], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 34}
-
label: 8T35
{'ab': 0, 'abstract_label': '128.928', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 928, 'gapidfull': '[128,928]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[4, 8]], [[1, 3], [5, 7]]], 'isomorphism': [5759, 23592, 34430, 592, 14493, 21410, 23616], 'label': '8T35', 'n': 8, 'name': '[2^4]D(4)', 'nilpotency': 4, 'num_conj_classes': 20, 'order': 128, 'parity': -1, 'pretty': '$C_2 \\wr C_2\\wr C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 7], [4, [4, 2], 7], [8, [4, 3], 6], [8, [8, 3], 1], [16, [8, 9], 3], [32, [8, 18], 1], [64, [8, 29], 1]], 'siblings': [[[8, 35], 7], [[16, 376], 4], [[16, 388], 4], [[16, 390], 4], [[16, 391], 4], [[16, 393], 4], [[16, 395], 4], [[16, 396], 4], [[16, 401], 4], [[32, 852], 4], [[32, 853], 2], [[32, 854], 2], [[32, 872], 2], [[32, 876], 4], [[32, 877], 2], [[32, 880], 2], [[32, 882], 2], [[32, 883], 4], [[32, 884], 2], [[32, 885], 2]], 'solv': 1, 'subfields': [[[2, 1], 1], [[4, 3], 1]], 't': 35}
-
label: 8T36
{'ab': 0, 'abstract_label': '168.43', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 43, 'gapidfull': '[168,43]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 2, 6, 3, 4, 5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [5808, 30750, 5759, 32794, 14493], 'label': '8T36', 'n': 8, 'name': 'E(8):F_21', 'nilpotency': -1, 'num_conj_classes': 8, 'order': 168, 'parity': 1, 'pretty': '$C_2^3:(C_7: C_3)$', 'prim': 1, 'quotients': [[3, [3, 1], 1], [21, [7, 3], 1]], 'siblings': [[[14, 11], 1], [[24, 283], 1], [[28, 27], 1], [[42, 26], 1]], 'solv': 1, 'subfields': [], 't': 36}
-
label: 8T37
{'ab': 0, 'abstract_label': '168.42', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 42, 'gapidfull': '[168,42]', 'gens': [[[1, 2, 4], [3, 6, 5]], [[1, 2, 3, 4, 5, 6, 8]], [[1, 6], [2, 3], [4, 5], [7, 8]]], 'isomorphism': [5864, 1677], 'label': '8T37', 'n': 8, 'name': 'L(8)=PSL(2,7)', 'nilpotency': -1, 'num_conj_classes': 6, 'order': 168, 'parity': 1, 'pretty': '$\\PSL(2,7)$', 'prim': 1, 'quotients': [], 'siblings': [[[7, 5], 2], [[14, 10], 2], [[21, 14], 1], [[24, 284], 1], [[28, 32], 1], [[42, 37], 1], [[42, 38], 2]], 'solv': 0, 'subfields': [], 't': 37}
-
label: 8T38
{'ab': 0, 'abstract_label': '192.201', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 201, 'gapidfull': '[192,201]', 'gens': [[[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [5, 6, 7]], [[4, 8]]], 'isomorphism': [512, 35481, 40319, 35152, 3420, 21410, 23616], 'label': '8T38', 'n': 8, 'name': '[2^4]A(4)', 'nilpotency': -1, 'num_conj_classes': 16, 'order': 192, 'parity': -1, 'pretty': '$C_2\\wr A_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [6, 1], 1], [12, [4, 4], 1], [24, [6, 6], 1], [96, [8, 33], 1]], 'siblings': [[[8, 38], 1], [[16, 425], 1], [[16, 427], 1], [[24, 288], 2], [[24, 425], 2], [[32, 2185], 2]], 'solv': 1, 'subfields': [[[4, 4], 1]], 't': 38}
-
label: 8T39
{'ab': 0, 'abstract_label': '192.1493', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1493, 'gapidfull': '[192,1493]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 6], [2, 3, 5, 4]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [28783, 31048, 26190, 26071, 32794, 14493, 28495], 'label': '8T39', 'n': 8, 'name': '[2^3]S(4)', 'nilpotency': -1, 'num_conj_classes': 13, 'order': 192, 'parity': 1, 'pretty': '$C_2^3:S_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1], [24, [4, 5], 3], [96, [8, 34], 1]], 'siblings': [[[8, 39], 5], [[16, 442], 3], [[24, 333], 6], [[24, 431], 2], [[32, 2213], 2]], 'solv': 1, 'subfields': [[[4, 5], 1]], 't': 39}
-
label: 8T40
{'ab': 0, 'abstract_label': '192.1494', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1494, 'gapidfull': '[192,1494]', 'gens': [[[1, 5], [4, 8]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [5, 6, 7]], [[2, 3], [4, 8], [6, 7]]], 'isomorphism': [21746, 12660, 23328, 21410, 34560, 7836, 23616], 'label': '8T40', 'n': 8, 'name': '1/2[2^4]S(4)', 'nilpotency': -1, 'num_conj_classes': 13, 'order': 192, 'parity': -1, 'pretty': '$Q_8:S_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1], [24, [4, 5], 3], [96, [8, 34], 1]], 'siblings': [[[8, 40], 1], [[16, 444], 1], [[16, 445], 1], [[24, 332], 2], [[24, 430], 2], [[32, 2215], 2]], 'solv': 1, 'subfields': [[[4, 5], 1]], 't': 40}
-
label: 8T41
{'ab': 0, 'abstract_label': '192.955', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 955, 'gapidfull': '[192,955]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]], [[1, 3], [4, 5, 6, 7]]], 'isomorphism': [10814, 23616, 10092, 36873, 5673, 5759, 14493], 'label': '8T41', 'n': 8, 'name': 'E(8):S_4=[E(4)^2:S_3]2=E(4)^2:D_12', 'nilpotency': -1, 'num_conj_classes': 14, 'order': 192, 'parity': 1, 'pretty': '$V_4^2:(S_3\\times C_2)$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 1], [12, [6, 3], 1], [24, [4, 5], 1], [48, [6, 11], 1]], 'siblings': [[[8, 41], 1], [[12, 108], 2], [[12, 109], 2], [[12, 110], 2], [[12, 111], 2], [[16, 435], 2], [[16, 436], 1], [[24, 516], 2], [[24, 517], 2], [[24, 518], 2], [[24, 519], 2], [[24, 520], 2], [[24, 521], 2], [[24, 522], 2], [[24, 523], 1], [[24, 524], 2], [[24, 525], 2], [[24, 526], 2], [[24, 527], 1], [[24, 528], 1], [[24, 529], 1], [[32, 2148], 1], [[32, 2149], 2]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 41}
-
label: 8T42
{'ab': 0, 'abstract_label': '288.1025', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1025, 'gapidfull': '[288,1025]', 'gens': [[[1, 3], [2, 8]], [[1, 2, 3]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [23616, 10092, 5772, 14433, 5673, 60, 86], 'label': '8T42', 'n': 8, 'name': '[A(4)^2]2', 'nilpotency': -1, 'num_conj_classes': 14, 'order': 288, 'parity': 1, 'pretty': '$A_4\\wr C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [3, 2], 1], [6, [6, 1], 1], [18, [6, 5], 1]], 'siblings': [[[12, 126], 1], [[12, 128], 1], [[12, 129], 1], [[16, 708], 1], [[18, 112], 1], [[18, 113], 1], [[24, 692], 1], [[24, 694], 1], [[24, 695], 1], [[24, 702], 1], [[24, 703], 1], [[24, 704], 1], [[32, 9306], 1], [[36, 316], 1], [[36, 318], 1], [[36, 456], 1], [[36, 457], 1], [[36, 458], 1], [[36, 459], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 42}
-
label: 8T43
{'ab': 0, 'abstract_label': '336.208', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 208, 'gapidfull': '[336,208]', 'gens': [[[1, 3, 2, 6, 4, 5]], [[1, 2, 3, 4, 5, 6, 8]], [[1, 6], [2, 3], [4, 5], [7, 8]]], 'isomorphism': [30670, 460], 'label': '8T43', 'n': 8, 'name': 'L(8):2=PGL(2,7)', 'nilpotency': -1, 'num_conj_classes': 9, 'order': 336, 'parity': -1, 'pretty': '$\\PGL(2,7)$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[14, 16], 1], [[16, 713], 1], [[21, 20], 1], [[24, 707], 1], [[28, 42], 1], [[28, 46], 1], [[42, 81], 1], [[42, 82], 1], [[42, 83], 1]], 'solv': 0, 'subfields': [], 't': 43}
-
label: 8T44
{'ab': 0, 'abstract_label': '384.5602', 'arith_equiv': 0, 'aut_label': '2.1', 'auts': 2, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 5602, 'gapidfull': '[384,5602]', 'gens': [[[1, 2, 3, 8], [4, 5, 6, 7]], [[1, 8], [4, 5]], [[4, 8]]], 'isomorphism': [21821, 21024, 4838, 14493, 28495, 592, 3420, 23616], 'label': '8T44', 'n': 8, 'name': '[2^4]S(4)', 'nilpotency': -1, 'num_conj_classes': 20, 'order': 384, 'parity': -1, 'pretty': '$C_2 \\wr S_4$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 1], [12, [6, 3], 1], [24, [4, 5], 1], [48, [6, 11], 1], [192, [8, 41], 1]], 'siblings': [[[8, 44], 3], [[16, 736], 2], [[16, 743], 2], [[16, 748], 2], [[16, 752], 2], [[24, 708], 4], [[24, 1151], 4], [[32, 9340], 1], [[32, 9355], 1], [[32, 9459], 4]], 'solv': 1, 'subfields': [[[4, 5], 1]], 't': 44}
-
label: 8T45
{'ab': 0, 'abstract_label': '576.8654', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 8654, 'gapidfull': '[576,8654]', 'gens': [[[1, 8], [4, 5]], [[1, 3], [2, 8]], [[1, 2, 3]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [734, 29388, 10080, 5772, 26, 86, 5673, 14433], 'label': '8T45', 'n': 8, 'name': '[1/2.S(4)^2]2', 'nilpotency': -1, 'num_conj_classes': 16, 'order': 576, 'parity': 1, 'pretty': '$(A_4\\wr C_2):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 2], [12, [6, 3], 2], [36, [6, 9], 1]], 'siblings': [[[12, 161], 1], [[12, 163], 1], [[12, 165], 2], [[16, 1032], 1], [[16, 1034], 1], [[18, 179], 1], [[18, 180], 1], [[18, 185], 2], [[24, 1490], 1], [[24, 1492], 1], [[24, 1493], 2], [[24, 1494], 2], [[24, 1495], 2], [[24, 1503], 1], [[24, 1504], 2], [[32, 34597], 2], [[32, 34598], 1], [[36, 759], 1], [[36, 760], 1], [[36, 762], 1], [[36, 763], 1], [[36, 774], 2], [[36, 775], 2], [[36, 960], 1], [[36, 961], 1], [[36, 962], 2], [[36, 963], 2]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 45}
-
label: 8T46
{'ab': 0, 'abstract_label': '576.8652', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 8652, 'gapidfull': '[576,8652]', 'gens': [[[1, 8], [4, 5]], [[1, 5], [2, 7, 3, 6], [4, 8]], [[1, 3], [2, 8]], [[1, 2, 3]]], 'isomorphism': [24336, 722, 10092, 12, 60, 86, 14433, 5673], 'label': '8T46', 'n': 8, 'name': '1/2[S(4)^2]2', 'nilpotency': -1, 'num_conj_classes': 13, 'order': 576, 'parity': -1, 'pretty': '$A_4^2:C_4$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [4, [4, 1], 1], [36, [6, 10], 1]], 'siblings': [[[12, 160], 1], [[12, 162], 1], [[16, 1030], 1], [[16, 1031], 1], [[18, 182], 1], [[18, 184], 1], [[24, 1489], 1], [[24, 1491], 1], [[24, 1505], 1], [[24, 1506], 2], [[24, 1508], 1], [[32, 34594], 1], [[36, 764], 1], [[36, 765], 1], [[36, 766], 1], [[36, 767], 1], [[36, 964], 1], [[36, 965], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 46}
-
label: 8T47
{'ab': 0, 'abstract_label': '1152.157849', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 157849, 'gapidfull': '', 'gens': [[[1, 2, 3, 8]], [[2, 3]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [14, 23616, 10814, 12, 10088, 86, 60, 5673, 14433], 'label': '8T47', 'n': 8, 'name': '[S(4)^2]2', 'nilpotency': -1, 'num_conj_classes': 20, 'order': 1152, 'parity': -1, 'pretty': '$S_4\\wr C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [8, [4, 3], 1], [72, [6, 13], 1]], 'siblings': [[[12, 200], 1], [[12, 201], 1], [[12, 202], 1], [[12, 203], 1], [[16, 1292], 1], [[16, 1294], 1], [[16, 1295], 1], [[16, 1296], 1], [[18, 272], 1], [[18, 273], 1], [[18, 274], 1], [[18, 275], 1], [[24, 2803], 1], [[24, 2804], 1], [[24, 2805], 1], [[24, 2806], 1], [[24, 2807], 1], [[24, 2808], 1], [[24, 2809], 1], [[24, 2810], 1], [[24, 2821], 1], [[24, 2826], 1], [[32, 96692], 1], [[32, 96694], 1], [[32, 96695], 1], [[32, 96696], 1], [[36, 1758], 1], [[36, 1759], 1], [[36, 1760], 1], [[36, 1761], 1], [[36, 1762], 1], [[36, 1763], 1], [[36, 1764], 1], [[36, 1765], 1], [[36, 1766], 1], [[36, 1767], 1], [[36, 1768], 1], [[36, 1769], 1], [[36, 1943], 1], [[36, 1944], 1], [[36, 1945], 1], [[36, 1946], 1]], 'solv': 1, 'subfields': [[[2, 1], 1]], 't': 47}
-
label: 8T48
{'ab': 0, 'abstract_label': '1344.11686', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 11686, 'gapidfull': '[1344,11686]', 'gens': [[[1, 3], [2, 8], [4, 6], [5, 7]], [[1, 2, 6, 3, 4, 5, 7]], [[1, 2], [5, 6]], [[1, 8], [2, 3], [4, 5], [6, 7]], [[1, 2, 3], [4, 6, 5]], [[1, 5], [2, 6], [3, 7], [4, 8]]], 'isomorphism': [18699, 28392], 'label': '8T48', 'n': 8, 'name': 'E(8):L_7=AL(8)', 'nilpotency': -1, 'num_conj_classes': 11, 'order': 1344, 'parity': 1, 'pretty': '$C_2^3:\\GL(3,2)$', 'prim': 1, 'quotients': [[168, [7, 5], 1]], 'siblings': [[[8, 48], 1], [[14, 34], 2], [[28, 153], 1], [[28, 159], 2], [[42, 210], 2], [[42, 211], 2]], 'solv': 0, 'subfields': [], 't': 48}
-
label: 8T49
{'ab': 0, 'abstract_label': '20160.a', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 0, 'gapidfull': '', 'gens': [[[1, 2], [3, 4, 5, 6, 7, 8]], [[1, 2, 3]]], 'isomorphism': [5193, 5760], 'label': '8T49', 'n': 8, 'name': 'A8', 'nilpotency': -1, 'num_conj_classes': 14, 'order': 20160, 'parity': 1, 'pretty': '$A_8$', 'prim': 1, 'quotients': [], 'siblings': [[[15, 72], 2], [[28, 433], 1], [[35, 36], 1]], 'solv': 0, 'subfields': [], 't': 49}
-
label: 8T50
{'ab': 0, 'abstract_label': '40320.a', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 0, 'gapidfull': '', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8]], [[1, 2]]], 'isomorphism': [5913, 5040], 'label': '8T50', 'n': 8, 'name': 'S8', 'nilpotency': -1, 'num_conj_classes': 22, 'order': 40320, 'parity': -1, 'pretty': '$S_8$', 'prim': 1, 'quotients': [[2, [2, 1], 1]], 'siblings': [[[16, 1838], 1], [[28, 502], 1], [[30, 1153], 1], [[35, 44], 1]], 'solv': 0, 'subfields': [], 't': 50}
-
label: 9T1
{'ab': 1, 'abstract_label': '9.1', 'arith_equiv': 0, 'aut_label': '9.1', 'auts': 9, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 1, 'gapid': 1, 'gapidfull': '[9,1]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8, 9]]], 'isomorphism': [46233], 'label': '9T1', 'n': 9, 'name': 'C(9)=9', 'nilpotency': 1, 'num_conj_classes': 9, 'order': 9, 'parity': 1, 'pretty': '$C_9$', 'prim': 0, 'quotients': [[3, [3, 1], 1]], 'siblings': [], 'solv': 1, 'subfields': [[[3, 1], 1]], 't': 1}
-
label: 9T2
{'ab': 1, 'abstract_label': '9.2', 'arith_equiv': 0, 'aut_label': '9.2', 'auts': 9, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 2, 'gapidfull': '[9,2]', 'gens': [[[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [138690, 77321], 'label': '9T2', 'n': 9, 'name': 'E(9)=3[x]3', 'nilpotency': 1, 'num_conj_classes': 9, 'order': 9, 'parity': 1, 'pretty': '$C_3^2$', 'prim': 0, 'quotients': [[3, [3, 1], 4]], 'siblings': [], 'solv': 1, 'subfields': [[[3, 1], 4]], 't': 2}
-
label: 9T3
{'ab': 0, 'abstract_label': '18.1', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 1, 'gapidfull': '[18,1]', 'gens': [[[1, 2, 3, 4, 5, 6, 7, 8, 9]], [[1, 8], [2, 7], [3, 6], [4, 5]]], 'isomorphism': [40319, 46233], 'label': '9T3', 'n': 9, 'name': 'D(9)=9:2', 'nilpotency': -1, 'num_conj_classes': 6, 'order': 18, 'parity': 1, 'pretty': '$D_{9}$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 1]], 'siblings': [[[18, 5], 1]], 'solv': 1, 'subfields': [[[3, 2], 1]], 't': 3}
-
label: 9T4
{'ab': 0, 'abstract_label': '18.3', 'arith_equiv': 0, 'aut_label': '3.1', 'auts': 3, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[18,3]', 'gens': [[[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[1, 2], [4, 5], [7, 8]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [267950, 77321], 'label': '9T4', 'n': 9, 'name': 'S(3)[x]3', 'nilpotency': -1, 'num_conj_classes': 9, 'order': 18, 'parity': -1, 'pretty': '$S_3\\times C_3$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [3, 2], 1], [6, [6, 1], 1]], 'siblings': [[[6, 5], 1], [[18, 3], 1]], 'solv': 1, 'subfields': [[[3, 1], 1], [[3, 2], 1]], 't': 4}
-
label: 9T5
{'ab': 0, 'abstract_label': '18.4', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 4, 'gapidfull': '[18,4]', 'gens': [[[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[1, 2], [3, 6], [4, 8], [5, 7]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [43034, 324885, 138690], 'label': '9T5', 'n': 9, 'name': 'S(3)[1/2]S(3)=3^2:2', 'nilpotency': -1, 'num_conj_classes': 6, 'order': 18, 'parity': 1, 'pretty': '$C_3^2:C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 4]], 'siblings': [[[18, 4], 1]], 'solv': 1, 'subfields': [[[3, 2], 4]], 't': 5}
-
label: 9T6
{'ab': 0, 'abstract_label': '27.4', 'arith_equiv': 0, 'aut_label': '3.1', 'auts': 3, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 4, 'gapidfull': '[27,4]', 'gens': [[[1, 4, 7], [2, 8, 5]], [[1, 2, 3, 4, 5, 6, 7, 8, 9]]], 'isomorphism': [263606, 171895], 'label': '9T6', 'n': 9, 'name': '1/3[3^3]3', 'nilpotency': 2, 'num_conj_classes': 11, 'order': 27, 'parity': 1, 'pretty': '$C_9:C_3$', 'prim': 0, 'quotients': [[3, [3, 1], 4], [9, [9, 2], 1]], 'siblings': [[[27, 5], 1]], 'solv': 1, 'subfields': [[[3, 1], 1]], 't': 6}
-
label: 9T7
{'ab': 0, 'abstract_label': '27.3', 'arith_equiv': 0, 'aut_label': '3.1', 'auts': 3, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 3, 'gapidfull': '[27,3]', 'gens': [[[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[3, 4, 5], [6, 8, 7]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [138690, 852, 77321], 'label': '9T7', 'n': 9, 'name': 'E(9):3=[3^2]3', 'nilpotency': 2, 'num_conj_classes': 11, 'order': 27, 'parity': 1, 'pretty': '$C_3^2:C_3$', 'prim': 0, 'quotients': [[3, [3, 1], 4], [9, [9, 2], 1]], 'siblings': [[[9, 7], 3], [[27, 3], 1]], 'solv': 1, 'subfields': [[[3, 1], 1]], 't': 7}
-
label: 9T8
{'ab': 0, 'abstract_label': '36.10', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 10, 'gapidfull': '[36,10]', 'gens': [[[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[3, 6], [4, 7], [5, 8]], [[1, 2], [4, 5], [7, 8]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [40442, 2592, 138690, 324885], 'label': '9T8', 'n': 9, 'name': 'S(3)[x]S(3)=E(9):D_4', 'nilpotency': -1, 'num_conj_classes': 9, 'order': 36, 'parity': -1, 'pretty': '$S_3^2$', 'prim': 0, 'quotients': [[2, [2, 1], 3], [4, [4, 2], 1], [6, [3, 2], 2], [12, [6, 3], 2]], 'siblings': [[[6, 9], 1], [[12, 16], 1], [[18, 9], 1], [[18, 11], 2], [[36, 13], 1]], 'solv': 1, 'subfields': [[[3, 2], 2]], 't': 8}
-
label: 9T9
{'ab': 0, 'abstract_label': '36.9', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 9, 'gapidfull': '[36,9]', 'gens': [[[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[1, 8, 2, 4], [3, 5, 6, 7]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [299582, 43034, 94762, 228132], 'label': '9T9', 'n': 9, 'name': 'E(9):4', 'nilpotency': -1, 'num_conj_classes': 6, 'order': 36, 'parity': 1, 'pretty': '$C_3^2:C_4$', 'prim': 1, 'quotients': [[2, [2, 1], 1], [4, [4, 1], 1]], 'siblings': [[[6, 10], 2], [[12, 17], 2], [[18, 10], 1], [[36, 14], 1]], 'solv': 1, 'subfields': [], 't': 9}
-
label: 9T10
{'ab': 0, 'abstract_label': '54.6', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 6, 'gapidfull': '[54,6]', 'gens': [[[1, 4, 7], [2, 8, 5]], [[1, 2, 3, 4, 5, 6, 7, 8, 9]], [[1, 8], [2, 7], [3, 6], [4, 5]]], 'isomorphism': [278250, 46233], 'label': '9T10', 'n': 9, 'name': '[3^2]S(3)_6', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 54, 'parity': 1, 'pretty': '$(C_9:C_3):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [3, 2], 1], [6, [6, 1], 1], [18, [6, 5], 1]], 'siblings': [[[18, 18], 1], [[27, 14], 1]], 'solv': 1, 'subfields': [[[3, 2], 1]], 't': 10}
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label: 9T11
{'ab': 0, 'abstract_label': '54.5', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 5, 'gapidfull': '[54,5]', 'gens': [[[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[1, 2], [3, 6], [4, 8], [5, 7]], [[3, 4, 5], [6, 8, 7]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [38871, 94762, 324885], 'label': '9T11', 'n': 9, 'name': 'E(9):6=1/2[3^2:2]S(3)', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 54, 'parity': 1, 'pretty': '$C_3^2 : C_6$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [3, 2], 1], [6, [6, 1], 1], [18, [6, 5], 1]], 'siblings': [[[9, 13], 1], [[18, 20], 1], [[18, 21], 1], [[18, 22], 1], [[27, 11], 1]], 'solv': 1, 'subfields': [[[3, 2], 1]], 't': 11}
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label: 9T12
{'ab': 0, 'abstract_label': '54.8', 'arith_equiv': 0, 'aut_label': '3.1', 'auts': 3, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 8, 'gapidfull': '[54,8]', 'gens': [[[3, 6], [4, 7], [5, 8]], [[3, 4, 5], [6, 8, 7]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [76485, 307544, 324885, 2592], 'label': '9T12', 'n': 9, 'name': '[3^2]S(3)', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 54, 'parity': -1, 'pretty': '$(C_3^2:C_3):C_2$', 'prim': 0, 'quotients': [[2, [2, 1], 1], [6, [3, 2], 4], [18, [9, 5], 1]], 'siblings': [[[9, 12], 3], [[18, 24], 4], [[27, 6], 1]], 'solv': 1, 'subfields': [[[3, 2], 1]], 't': 12}
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label: 9T13
{'ab': 0, 'abstract_label': '54.5', 'arith_equiv': 0, 'aut_label': '1.1', 'auts': 1, 'bound_quotients': 47, 'bound_siblings': 47, 'cyc': 0, 'gapid': 5, 'gapidfull': '[54,5]', 'gens': [[[1, 2], [3, 5], [6, 7]], [[1, 2, 9], [3, 4, 5], [6, 7, 8]], [[3, 4, 5], [6, 8, 7]], [[1, 4, 7], [2, 5, 8], [3, 6, 9]]], 'isomorphism': [313094, 852, 77321], 'label': '9T13', 'n': 9, 'name': 'E(9):D_6=[3^2:2]3=[1/2.S(3)^2]3', 'nilpotency': -1, 'num_conj_classes': 10, 'order': 54, 'parity': -1, 'pretty': '$C_3^2 : S_3 $', 'prim': 0, 'quotients': [[2, [2, 1], 1], [3, [3, 1], 1], [6, [3, 2], 1], [6, [6, 1], 1], [18, [6, 5], 1]], 'siblings': [[[9, 11], 1], [[18, 20], 1], [[18, 21], 1], [[18, 22], 1], [[27, 11], 1]], 'solv': 1, 'subfields': [[[3, 1], 1]], 't': 13}
