In fact, I have a copy of a preprint by Feit of this paper. I have not checked the results, but here is what Feit says: the group of signed permutation matrices is of maximal order as a finite subgroup of ${\rm GL}(n,\mathbb{Q})$, except in the following cases (Feit's Theorem A).

$n = 2, W(G_{2})$ of order $12$. 

$n = 4, W(F_{4}),$ order $1152$.

$n = 6, W(E_{6}) \times C_{2},$ order $103680.$

$n = 7, W(E_{7}),$ order $2903040.$

$n = 8, W(E_{8}),$ order $696729600$.

$n = 9, W(E_{8}) \times W(A_{1})$, order $1393459200$ (reducible).

$n = 10, W(E_{8}) \times W(G_{2}),$ order $8360755200$ (reducible).

Maximal order of finite subgroups of $GL(n,Z)$
i think there is a problem with the video shortcode.

When i use [video src="" height="400"] the 400px height not work. The width work correctly but the height nothing.

Is it a bug?
