Exotic cohomology for $GL_n(\mathbb Z[1/2])$ 
W. G. Dwyer
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 

Proc. Amer. Math. Soc. 126 (1998), 2159-2167.

Abstract. We show that for $n = 32$ the mod $2$ group cohomology of 
$GL_n(\mathbb Z[1/2])$ is not detected on diagonal matrices.