Chern classes and extraspecial groups

Summary The mod-p cohomology ring of the extraspecialp-group of exponentp is studied for oddp. 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. The support of the Deutsche Forschungsgemeinschaft and the Max Kade Foundation is gratefully acknowledged, as is the kind hospitality of the ETH Zürich. The support of the Eidgen?ssische Technische Hochschule in Zürich and of the Leibniz Fellowship Programme is acknowledged with thanks. This article was processed by the author using theLatex style filecljour1 from Springer-Verlag.