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!