Let G be a finite non-abelian group with no elements of order 2, and let H be a normal subgroup containing the commutator subgroup of G. Show that the product of all elements of G (written in any order) lies in H.

I am really lost! I would start by stating that: Since H is normal and contains the commutator subgroup of G then G/H is a commutative group. So abH = aH bH = bH aH = baH.

but I don't really know where to go from here