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.
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Unless I miscomputed, 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 2Sylow subgroups and 7 3Sylow subgroups. 

