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We compute the Chern subgroup of the 4-th integral cohomology group of a certain classifying space and show that it is a proper subgroup.
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A. Tripathy, Further counterexamples to the integral hodge conjecture, preprint, arXiv:1601.06170
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B. Antieau, On the integral Tate conjecture for finite fields and representation theory, Algebr. Geom. 3
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