Why $S_4$ is not isomorphic to $D_{12}$? where $S_4$ is symmetric group and $D_{12}$ is dihedral group of order $12$.here number of element are same $S_4$ has $4!=24$ elements and $D_{12}$ has also $2n$ means $12(2)=24$ elements. but i can't find that property which holds in one of this group but another doesn't has that property.please help me thanks in advance.
via Recent Questions - Mathematics - Stack Exchange http://math.stackexchange.com/questions/289651/s-4-is-not-isomorphic-to-d-12
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