Algebra group implies power degree group for field size

Statement
Suppose $$N$$ is a nilpotent associative algebra over a finite field $$\mathbb{F}_q$$ for a prime power $$q$$, and $$G$$ is the algebra group corresponding to $$N$$. Then, $$G$$ is a q-power degree group: all its degrees of irreducible representations are powers of $$q$$.