We define and study supercharacters of the classical finite unipotent groups of types B n (q),
C n (q) and D n (q). We show that the results we proved in 2006 remain valid over any finite
field of odd characteristic. In particular, we show how supercharacters for groups of those
types can be obtained by restricting the supercharacter theory of the finite unitriangular
group, and prove that supercharacters are orthogonal and provide a partition of the set of all
irreducible characters. In addition, we prove that the unitary vector space spanned by all the …