  We discuss necessary conditions for a compact quantum group to act on the
algebra of noncommutative $n$-torus $\mathbb{T}_\theta^n$ in a filtration
preserving way in the sense of Banica and Skalski. As a result, we construct a
family of compact quantum groups $\mathbb{G}_\theta=(A_\theta^n,\Delta)$ such
that for each $\theta$, $\mathbb{G}_\theta$ is the final object in the category
of all compact quantum groups acting on $\mathbb{T}_\theta^n$ in a filtration
preserving way. We describe in details the structure of the C*-algebra
$A_\theta^n$ and provide a concrete example of its representation in bounded
operators. Moreover, we compute the Haar measure of $\mathbb{G}_\theta$. For
$\theta=0$, the quantum group $\mathbb{G}_0$ is nothing but the classical group
$\mathbb{T}^n\rtimes S_n$, where $S_n$ is the symmetric group. For general
$\theta$, $\mathbb{G}_\theta$ is still an extension of the classical group
$\mathbb{T}^n$ by the classical group $S_n$. It turns out that for $n=2$, the
algebra $A_\theta^2$ coincides with the algebra of the quantum double-torus
described by Hajac and Masuda. Using a variation of the little subgroup method
we show that irreducible representations of $\mathbb{G}_\theta$ are in
one-to-one correspondence with irreducible representations of
$\mathbb{T}^n\rtimes S_n$.
