Is there a group epimorphism $\mathbb{R} \to S_3$?

Question

I had to found some group epimorphisms and I stucked with this example.

Is there an epimorphism from a group $(R,+)$ - real numerbes with addition onto a group $(S_3,\circ)$?

Answer 1

Hint: Let $x \in \mathbb R$. Write $x=6y$. If $y \mapsto \sigma$, then $x \mapsto \sigma^6 = e$.

This argument works for all finite groups, not just $S_3$.