Hello. I have been asked to prove the following:

If is a nontrivial normal subgroup of a nilpotent group , then is nontrivial.

I attempted to take the factor group (since it too is nilpotent) and try to deal with the image of under the canonical homomorphism, but I can't get the result to come out.

This is extremely frustrating, and thus, I would appreciate any suggestions you may have. (Though, I am not necessarily searching for a complete solution.)

Thank you.