1. ## Isomorphic?

How do I show whether the pair of groups $S_{5},D_{60}$ is isomorphic?

I know that the order of the two groups is 120, they are both non-commutative, they are both non-cyclic. But I believe they are not isomorphic since I can't really find a function that does the trick.

K

2. The only element $\sigma \in S_n$ with $n\geq 3$ that has a property that $\sigma \tau = \tau \sigma$ i.e. it commutes with everything, is $\sigma = i$, i.e. the identity element.*

Now is that true for $D_n$, i.e. it has a trivial center? I think not. So they are non-isomorphic.

*)If you every learned the meaning of "center" we will say the center of $S_n$ is trivial for $n\geq 3$.