Is $ \begin{bmatrix} 1 & * & * \\ 0&1&*\\0&0&1 \end{bmatrix} $ a Sylow $p$-subgroup of $Gl_3 \left(\mathbb F_p\right)$? If so, how would I describe a composition series for this Sylow $p$-subgroup?
Or is $L = \left\{ \begin{bmatrix} 1 & 0 & 0\\ a & 1 & 0\\ c & b & 1\\ \end{bmatrix} : a, b, c \in \Bbb F_p \right\} $ a better example of such a Sylow $p$-subgroup? How would I describe a composition series for this?
Any help greatly appreciated.