Finding the Galois group of $\mathbb{Q}(2^{1/p},\zeta_{2n})$

Question

How to find the Galois group of the extension $\mathbb{Q}(2^{1/p},\zeta_{2n})$ of $\mathbb{Q}$? Here $n$ is a positive integer, and $p$ is an odd prime factor of $n$.