  Symmetrization of topologically ordered wavefunctions is a powerful method
for constructing new topological models. Here, we study wavefunctions obtained
by symmetrizing quantum double models of a group $G$ in the Projected Entangled
Pair States (PEPS) formalism. We show that symmetrization naturally gives rise
to a larger symmetry group $\tilde G$ which is always non-abelian. We prove
that by symmetrizing on sufficiently large blocks, one can always construct
wavefunctions in the same phase as the double model of $\tilde G$. In order to
understand the effect of symmetrization on smaller patches, we carry out
numerical studies for the toric code model, where we find strong evidence that
symmetrizing on individual spins gives rise to a critical model which is at the
phase transitions of two inequivalent toric codes, obtained by anyon
condensation from the double model of $\tilde G$.
