  The mod-p cohomology ring of the extraspecial p-group of exponent p is
studied for odd p. We investigate the subquotient ch(G) generated by Chern
classes modulo the nilradical. The subring of ch(G) generated by Chern classes
of one-dimensional representations was studied by Tezuka and Yagita. The
subring generated by the Chern classes of the faithful irreducible
representations is a polynomial algebra. We study the interplay between these
two families of generators, and obtain some relations between them.
