  The symmetric homology of a unital associative algebra $A$ over a commutative
ground ring $k$, denoted $HS_*(A)$, is defined using derived functors and the
symmetric bar construction of Fiedorowicz. In this paper we show that $HS_*(A)$
admits homology operations and a Pontryagin product structure making $HS_*(A)$
an associative commutative graded algebra. This is done by finding an explicit
$E_{\infty}$ structure on the standard chain groups that compute symmetric
homology.
