Proof that $S_3$ isomorphic to $D_3$ So I'm asked to prove that $$S_{3}\cong D_{3}$$ where $D_3$ is the dihedral group of order $6$. I know how to exhibit the isomorphism and verify every one of the $6^{2}$ pairs, but that seems so long and tedious, I'm not sure my fingers can withstand the brute force. Is there a better way?

Hint:   $S_3=\langle(1,2,3),(1,2)\rangle$ and $D_3=\langle a,b\rangle$ set $\phi(a)=(1,2,3)$ and $\phi(b)=(1,2)$ i.e send generaters to generaters.
Note: Choose $a$ from the ones of order $3$ and b from the ones of order $2$.
