  Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are
used in the context of describing certain invariants for complex algebraic
surfaces. He proved that these functors are connected to the theory of central
extensions and Schur multipliers. In this work we relate $K$ and $\tilde K$ to
a group functor $\tau$ arising in the construction of the non-abelian exterior
square of a group. In contrast to $\tilde K$, there exist efficient algorithms
for constructing $\tau$, especially for polycyclic groups. Supported by
computations with the computer algebra system GAP, we investigate when $K(G,3)$
is a quotient of $\tau(G)$, and when $\tau(G)$ and $\tilde K(G,3)$ are
isomorphic.
