Is the Dihedral Group of order $24$ isomorphic to the Symmetric Group on $4$ elements? [closed]

abstract-algebra group-theory finite-groups group-isomorphism

Is the Dihedral Group of order $24$ isomorphic to the Symmetric Group of $4$ elements?


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.)

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