We prove that the Scott module whose vertex is isomorphic to a direct product of generalized quaternion $2$-group and cyclic Brauer indecomposable. This result generalizes similar results which are obtained for abelian, dihedral, quaternion, semidihedral wreathed vertices.

The dihedral group is defined by 〈x, y | x = y = e, xy = yx−1〉 for n ≥ 3 and has order 2n. In this note four families of 2-critical sets are presented for the Latin square based on this group for even n.

In a paper of Kedlaya and Medvedovsky [KM19] , the number distinct dihedral mod 2 modular representations prime level N was calculated, conjecture on dimension space weight forms giving rise to each representation stated. this we prove conjecture.