(i) Compute the fundamental group of the Klein bottle. Show that this group is not abelian, for example by defining a suitable homomorphism to the symmetric group $S_{3}$.

(ii) Let $X$ be the closed orientable surface of genus 2 . How many (connected) double coverings does $X$ have? Show that the fundamental group of $X$ admits a homomorphism onto the free group on 2 generators.