Conjugacy Class in Symmetric Group
This question might be duplicate because of a representation theory
question. I don't know representation theory enough so I didn't tried to
check that section. Please notify.
I heard and experienced that if $s_1,s_2 \in Sym(n)$, then there exists a
$k \in Sym(n)$ such that $k^{-1}s_1k = s_2 \iff s_1$ and $s_2$ has same
cycle type.
I tried to proof this statement but in the middle of it someone told me it
has really short proof so I started to trying to find it but I couldn't. I
hope you can help me and find that short proof.
Thanks for any help.
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