  We show that a semisimple Hopf algebra A is group theoretical if and only if
its Drinfeld double is a twisting of the Dijkgraaf-Pasquier-Roche quasi-Hopf
algebra D^{omega}(Sigma), for some finite group Sigma and some 3-cocycle omega
on Sigma. We show that semisimple Hopf algebras obtained as bicrossed products
from an exact factorization of a finite group Sigma are group theoretical. We
also describe their Drinfeld double as a twisting of D^{omega}(Sigma), for an
appropriate 3-cocycle omega coming from the Kac exact sequence.
