Let $E_7$ denote the split group of type $E_7$. Assume $G := \xi\overline{G}$ is a semisimple algebraic group over a field $k$ with characteristic zero for some $\xi \in H^1(k,E_7)$. Let $r(G)$ $\in$ $H^3(k,\mu_2)$ be the even part of the Rost Invariant. Assume further that the Tits Index of $G$ has all but three points circled (these are necessarily number $2,5,7$ in Bourbaki notation).

Note that the classical Rost invariant is defined for simply connected groups. In the adjoint case one needs to consider some generalized version.

Question: Is $r(G)$ a pure symbol in $H^3(k,\mu_2)$?

For me pure symbol in is an element of the form $(a) \cup (b) \cup (c)$.