  Each orthogonal group $\OO(n)$ has a nontrivial $\GL(1)$-extension, which we
call $\GPin(n)$. The identity component of $\GPin(n)$ is the more familiar
$\GSpin(n)$, the general Spin group. We prove that the restriction to
$\GPin(n-1)$ of an irreducible admissible representation of $\GPin(n)$ over a
nonarchimedean local field of characteristic zero is multiplicity free and also
prove the analogous theorem for $\GSpin(n)$. Our proof uses the method of
Aizenbud, Gourevitch, Rallis and Schiffman, who proved the analogous theorem
for $\OO(n)$, and Waldspurger, who proved that for $\SO(n)$.
  We also give an explicit description of the contragredient of an irreducible
admissible representation of $\GPin(n)$ and $\GSpin(n)$, which is needed to
apply their method to our situations.
