Cn Weyl group
= Cn Weyl group
{c}
{title2=$W(C_n)\cong(\mathbb Z/2\mathbb Z)^n\rtimes S_n$}
The <Weyl group> of the <Cn root system> is the <signed symmetric group>. A <Weyl reflection> in $2\varepsilon_i$ changes the sign of coordinate $i$; one in $\varepsilon_i-\varepsilon_j$ interchanges coordinates $i,j$; one in $\varepsilon_i+\varepsilon_j$ interchanges and negates both coordinates. These generate all independent sign changes and all <permutations>, giving order $2^nn!$.