# Is the quotient of a toric variety by a finite group still toric

Suppose $X$ is a toric variety with fan $\Sigma$, and the lattice of its torus is $N$. Suppose there is a representation of finite group $G$, $$\phi:G \rightarrow \text{GL}(N \otimes_{\mathbb{Z}} \mathbb{R})$$ which maps the lattice points of $N$ to lattice points of $N$, and maps the cones of $\Sigma$ to the cones of $\Sigma$.
Question: is the quotient variety $X/G$ (which exists from GIT) still a toric variety?

I guess the answer is yes? Are there references about how to construct the fan of $X/G$?

Edit: I have asked this question on MO.

https://mathoverflow.net/questions/297470/is-the-quotient-of-a-toric-variety-by-a-finite-group-still-toric