  We consider gauge theories of non-Abelian $finite$ groups, and discuss the
1+1 dimensional lattice gauge theory of the permutation group $S_N$ as an
illustrative example. The partition function at finite $N$ can be written
explicitly in a compact form using properties of $S_N$ conjugacy classes. A
natural large-$N$ limit exists with a new 't Hooft coupling, $\lambda=g^2 \log
N$. We identify a Gross-Witten-Wadia-like phase transition at infinite $N$, at
$\lambda=2$. It is first order. An analogue of the string tension can be
computed from the Wilson loop expectation value, and it jumps from zero to a
finite value. We view this as a type of large-$N$ (de-)confinement transition.
Our holographic motivations for considering such theories are briefly
discussed.
