Consider the orthogonal group $O(2l+1)$ ($l \geq 1$), is there an matrix in $O(2l+1)$ with its minimal polynomial being $(x-1)^{2l+1}$?
A similar question has been asked for the $O(2l)$ (this link : Minimal polynomial of unipotents in orthogonal group) . So I am asking now for the $2l+1$ case.