  We introduce a single tau function that represents the CKP hierarchy into a
generalized Hirota "bilinear" equation. The actions on the tau function by
additional symmetries for the hierarchy are calculated, which involve strictly
more than a central extension of the $w^C_\infty$-algebra. As an application,
for Drinfeld-Sokolov hierarchies of type C that are equivalent to certain
reductions of the CKP hierarchy, their Virasoro symmetries are proved to be
non-linearizable when acting on the tau function.
