  We define the superclasses for a classical finite unipotent group $U$ of type
$B_{n}(q)$, $C_{n}(q)$, or $D_{n}(q)$, and show that, together with the
supercharacters defined in a previous paper, they form a supercharacter theory.
In particular, we prove that the supercharacters take a constant value on each
superclass, and evaluate this value. As a consequence, we obtain a
factorization of any superclass as a product of elementary superclasses. In
addition, we also define the space of superclass functions, and prove that it
is spanned by the supercharacters. As as consequence, we (re)obtain the
decomposition of the regular character as an orthogonal linear combination of
supercharacters. Finally, we define the supercharacter table of $U$, and prove
various orthogonality relations for supercharacters (similar to the well-known
orthogonality relations for irreducible characters).
