More group cohomology

My advisor told me to go hit [tex]D_8[/tex] and [tex]U(\mathbb H)[/tex] as my next two cohomology calculation projects; try to do them with resolutions by hand so that I get a feeling for what's going on. After failing spectacularily both at getting a resolution of [tex]\mathbb F_2[/tex] with [tex]\mathbb F_2D_8[/tex], he walked me through his Shiny! Gr