I have two confusion in sylow theorem formula
$1.$Order of a $n$ sylow subgroup in $GL_n (\mathbb{F_p})= \frac{\prod_ {i=0}^{n-1} (p^n -p^i)}{(p-1)^n p^{\frac {n(n-1)}{2}}}$
$2.$ Order of a $q-$sylow subgroups in $GL_n (\mathbb{F_p})=$the highest power of $q$ dividing $\prod_ {i=0}^{n-1} (p^n -p^i)$
Edits : Note : Here $n$ is prime number for cases $1$
Is the given above formula is true /false ?