The cohomology of exotic 2-local finite groups

There exist spaces BSol(q) which are the classifying spaces of a family of 2-local finite groups based on certain fusion system over the Sylow 2-subgroups of Spin(7)(q). In this paper we calculate the cohomology of BSol( q) as an algebra over the Steenrod algebra A(2). We also provide the calculation of the cohomology algebra over A2 of the finite group of Lie type G(2)(q).