6.14. Let TT € S8 be the permutation defined by π(1) = 3, TT (2) = 8, TT (5) = 6, TT (6) = 1, (a) Prove that has order 4. {е, π, T², T³}. TT (3) = 5, π(7) = 7, T(4) = 4, TT (8) = 2. Let G be the subgroup for SÅ generated by ; i.e., G = (π) = (b) Describe all of the orbits of G, as was done in Example 6.18. (c) Let X = {1, 2, 3, 4, 5, 6, 7, 8}, so G acts on X. For each k E X, describe the stabilizer Gk.

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