  Let $S_{2m}$ be the symmetric group, $h=(1\ 2)(3\ 4)\cdots(2m-1\ 2m)$ and
$H=C(h)$. We consider the structure of $gHg^{-1}\cap H$ for any $g\in S_{2m}$.
We prove the permutations $g$ which makes $gHg^{-1}\cap H$ have size of
polynomial in $m$ have density zero.
