= Symplectic parabolic subgroup
The stabilizer of a totally isotropic $k$-space in a finite symplectic space also stabilizes its orthogonal complement. Its block decomposition has a unipotent normal subgroup $Q$ and a block-diagonal complement $L\cong\operatorname{GL}_k(q)\times\operatorname{Sp}_{2m-2k}(q)$. The paired $k$-space carries the contragredient action. A row-vector convention gives upper-triangular blocks; a column-vector convention transposes the arrangement. The <unipotent radical count for a symplectic parabolic subgroup> yields its order.
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