I'm looking for a classification of $3$-forms over a real vector space of dimension $7$ as for the $3$-forms in dimension $6$. References on the latter case are R. Bryant On the geometry of almost complex $6$-manifolds available here and P. Baier's PhD thesis available here.

I found this by Cohen and Helminik Trilinear alternating forms on a vector space of dimension $7$ available here but I was wondering if it is possible to find in literature the real case explicitly done.