Let $G$ be a finite subgroup of $\mathrm{GL}_n(\mathbb{k})$ where $\mathbb{k}$ is an algebraically closed field. Choose the correct statement(s) from below:
(A) Every element of $G$ is diagonalizable;
(B) Every element of $G$ is diagonalizable if $\mathbb{k}$ is an algebraic closure of $\mathbb{Q}$;
(C) Every element of $G$ is diagonalizable if $\mathbb{k}$ is an algebraic closure of $\mathbb{F}_p$;
(D) There exists a basis of $\mathbb{k}^n$ with respect to which every element of $G$ is a diagonal matrix.