  We show how to compute a certain group of equivalence classes of invariant
Drinfeld twists on the algebra of a finite group G over a field k of
characteristic zero. This group is naturally isomorphic to the second lazy
cohomology group of the Hopf algebra of k-valued functions on G.
  When k is algebraically closed, the answer involves the group of outer
automorphisms of G induced by conjugation in the group algebra as well as the
set of all pairs (A, b), where A is an abelian normal subgroup of G and b is a
k^*-valued G-invariant non-degenerate alternating bilinear form on the
Pontryagin dual of A.
  We give a number of examples.
