Galois group of $T^3-2$ over $ \mathbb{F}_5$

Question

What is the galois group of $T^3-2$ over $\mathbb{F}_5$?

I dont really see a way to find this group. I saw it for $\mathbb{Q}$ but not $\mathbb{F}_5$.

Answer 1

Hint: Since $2=3^3$ in $\mathbb{F}_5$, the splitting field of $T^3-2$ is the same as the splitting field of $T^3-1$.