Source: /cirosantilli/finite-general-linear-group

= Finite general linear group
{title2=$GL(n, F_m)$}

= $GL(n, m)$
{synonym}
{title2}

<general linear group> over a <finite field> of order $m$. Remember that due to the <classification of finite fields>, there is one single field for each <prime power> $m$.

Exactly as over the <real numbers>, you just put the finite field elements into a $n \times n$ matrix, and then take the invertible ones.