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We give a stratification of the GIT quotient of the Grassmannian $G_{2,n}$modulo the normaliser of a maximal torus of $SL_{n}(k)$ with respect to theample generator of the Picard group of $G_{2,n}$. We also prove that the flagvariety $GL_{n}(k)/B_{n}$ can be obtained as a GIT quotient of$GL_{n+1}(k)/B_{n+1}$ modulo a maximal torus of $SL_{n+1}(k)$ for a suitablechoice of an ample line bundle on $GL_{n+1}(k)/B_{n+1}$.

Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups