The cohomology of the Mathieu group \(M_{22}\) (Q1804907)

The author describes the structure of the mod 2 cohomology \(H^* (M_{22}; {\mathbf F}_2)\) of the sporadic group \(M_{22}\). In particular, the kernel of the restriction map from \(H^*(M_{22}; {\mathbf F}_2)\) to the cohomology of conjugacy classes of extremal elementary 2-subgroups is explicitly determined.