A student I'm helping gave me a question.
Q: Give an example of a group G with a normal subgroup N such that N and G/N are abelian, but G is not abelian.
I'm fairly sure there is a dihedral group with this property but i don't have time to find an explicit example.
Can someone help please?
Side note: If we weaken the conditions slightly and replace abelian by solvable no example exists.