Nilpotent lie algebras with a small second derived quotient

Here we find the structure of nilpotent Lie algebras L with dim(L'/L'')=3 and L''0. Following the pattern of results of Csaba Schneider in p-groups, we show that L is the central direct sum of ideals H and U, where U is the direct sum of a generalized Heisenberg Lie algebra and an abelian Lie algebra. We then find over the complex numbers that H falls into one of fourteen isomorphism classes.