Presentation of wreath product $G=S_3 \wr S_3$ of symmetric groups. What is the isomorphism type of $G/[G,G]$?

Question

I'm trying to answer the first part of a group theory question as revision for an exam that goes as follows;

Let $G = S_3 \wr S_3$, the permutational wreath product of two symmetric groups of degree three. Give a presentation for $G$ and determine the isomorphism type of $G/[G, G]$.

I'm not sure how to go about finding generators for the wreath product itself.

Is there a method for combining the generators of the symmetric groups to form generators for the wreath prouct?

Any pointers would be much appreciated, thanks in advance!