2-modular representation theory of GL3 of F2 (${\mathrm{GL}}_3({\mathbb{F}}_2)$ in characteristic two)

The simple modules have dimensions $1,3,3,8$. The eight-dimensional simple is projective and forms a defect-zero block; the other three simples belong to the principal block. The decomposition and Cartan matrices are computed by restricting the six ordinary irreducible characters to the four odd-order conjugacy classes.