TITLE: Generators of the Symmetric group $S_3$
QUESTION [7 upvotes]: I am trying to find the generator(s) of the Symmetric Group $S_3$ and I have attempted this via brute force by listing the permutations of $S_3$ and composing and repeating them but I have not found any generators.
- thanks

REPLY [3 votes]: Regarding to @Sanath's post and that you already knew the structure of $S_3$'s structure, we may treat the group with the following presentation:
$$\langle a,b\mid a^2=b^3=(ab)^2=1\rangle$$ It is good to know that $S_3=D_6$, the dihedral group of order $6$.