  We study properties of symmetric fusion categories in characteristic $p$. In
particular, we introduce the notion of a super Frobenius-Perron dimension of an
object $X$ of such a category, and derive an explicit formula for the Verlinde
fiber functor $F(X)$ of $X$ (defined by the second author) in terms of the
usual and super Frobenius-Perron dimension of $X$. We also compute the
decomposition of symmetric powers of objects of the Verlinde category,
generalizing a classical formula of Cayley and Sylvester for invariants of
binary forms. Finally, we show that the Verlinde fiber functor is unique, and
classify braided fusion categories of rank two and triangular semisimple Hopf
algebras in any characteristic.
