Is the Dihedral Group of order $24$ isomorphic to the Symmetric Group of $4$ elements?
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Look at the largest cyclic subgroup possible in both the cases. In the dihedral case we have a cyclic subgroup of order 12. It is not possible in $S_4$.
(Your wording symmetric group with 4 elements does not conform to the convention. It should be on 4 elements.)
P Vanchinathan
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2Nice, I think it's easier to say: $D_{24}$ has an element of order of $12$, while $S_4$ does not. – Asinomás Jan 17 '16 at 16:00