Weyl group of Dn
= Weyl group of Dn
{c}
{title2=$W(D_n)\cong(\mathbb Z/2\mathbb Z)^{n-1}\rtimes S_n$}
The <Weyl group> of the <Dn root system> consists of coordinate permutations together with an even number of sign changes. Reflection in $\varepsilon_i-\varepsilon_j$ swaps coordinates $i,j$; reflection in $\varepsilon_i+\varepsilon_j$ swaps them and negates both. These generate all even signed permutations, giving order $2^{n-1}n!$.