Let $p$ and $q$ be prime divisors of finite group $G$. Also let $n\_{p}$ be
the number of Sylow $p$-subgroups of $G$ . Is there any example such that
$n\_{p}=n\_{q}\neq 1$? Thanks in advance.



Question on the equal Sylow number
Unless I mis-computed, this happens in the group of affine transformations ($x \mapsto ax+b$ with $a\neq 0$) over the field of 7 elements. There seem to be 7 2-Sylow subgroups and 7 3-Sylow subgroups.


