In this paper, the integral
cohomology ring of a Blackburn’s type III rank2p-group (p > 3) (the rank of a
p-group is the rank of a maximal elementary abelian subgroup) is computed and the
even dimensional generators are expressed in terms of Chern classes of certain group
representations. Then this group satisfies Atiyah’s conjecture on the coincidence of
topological and algebraic filtrations defined on the complex representation ring of the
group.