The Weyl Group of $F_4$ is of order $1152=2^{7} \cdot 3^{2}$. By Burnside's theorem the group is solvable.
Is there a way to see solvability from the root system? Is it possible to see the order of the group there?
The Weyl Group of $F_4$ is of order $1152=2^{7} \cdot 3^{2}$. By Burnside's theorem the group is solvable.
Is there a way to see solvability from the root system? Is it possible to see the order of the group there?