Editing Generalized permutation matrix (section)

===Properties===
* It is the [[Coxeter group]] <math>B_n</math>, and has [[order (group theory)|order]] <math>2^n n!</math>.
* It is the symmetry group of the [[hypercube]] and (dually) of the [[cross-polytope]].
* Its [[index of a subgroup|index]] 2 subgroup of matrices with determinant equal to their underlying (unsigned) permutation is the Coxeter group <math>D_n</math> and is the symmetry group of the [[demihypercube]].
* It is a subgroup of the [[orthogonal group]].