Representations of the double Burnside algebra and cohomology of the extraspecial p-group II

Let E be the extraspecial p  -group of order p3p3 and exponent p where p is an odd prime. We determine the mod p   cohomology H⁎(X,Fp)H⁎(X,Fp) of a summand X in the stable splitting of p-completed classifying space BE. In the previous paper (Hida and Yagita (2014) [7]), we determined this cohomology modulo nilpotence. In this paper, we consider the whole of the cohomology. Moreover, we consider the stable splittings of BG for some finite groups with Sylow p-subgroup E   related to the three dimensional linear group L3(p)L3(p).