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Let $S_3$ be the symmetric group on $3$ symbols, represented as the group of permutations of the set $\{1,2,3\}$.
Let $(\cdot)$ be the neutral element of $S_3$.

Let $\varphi:S_3\rightarrow G$ be a group homomorphism of $S_3$ to another group $G$.

The group
Select Option $\{(\cdot)\}$$\mathbb{Z}/2\mathbb{Z}$$\mathbb{Z}/3\mathbb{Z}$$S_3$
can not be isomorphic to the kernel of $\varphi$. The group
Select Option $\{(\cdot)\}$$\mathbb{Z}/2\mathbb{Z}$$\mathbb{Z}/3\mathbb{Z}$$S_3$
can not be isomorphic to the image of $\varphi$.
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