If $\mathbb{F}_q$ is a finite field with $q$ elements, then the general linear group $\operatorname{GL}(n, \mathbb{F}_q)$ over the field $\mathbb{F}_q$

1. is a finite group of order $\lvert \operatorname{GL}(n, \mathbb{F}_q) \rvert = \prod_{i=0}^{n-1}(q^n-q^i)$ and
2. $[\operatorname{GL}(n,\mathbb{F}_q),\operatorname{GL}(n,\mathbb{F}_q)] = \operatorname{SL}(n,\mathbb{F}_q)$ where $[,]$ is the commutator bracket with the exception of $\operatorname{SL}(2,\mathbb{F}_2)$