There is a nonabelian subgroup T of $\displaystyle S_{3} \times Z_{4}$ of order 12 generated by elements a, b such that $\displaystyle |a|= 6, a^{3}=b^{2}, ba=a^{-1}b$.

What are the generaters a, b for the above group T such that T = <a , b> and what are the elements of T?