  In this article, we explore the problem of determining isomorphisms between
the twisted complex group algebras of finite $p$-groups. This problem bears
similarity to the classical group algebra isomorphism problem and has been
recently examined by Margolis-Schnabel. Our focus lies on a specific invariant,
referred to as the generalized corank, which relates to the twisted complex
group algebra isomorphism problem. We provide a solution for non-abelian
$p$-groups with generalized corank at most three.
