Editing Generalized permutation matrix (section)

===Subgroups===
* The subgroup where all entries are 1 is exactly the [[permutation matrices]], which is isomorphic to the symmetric group.
* The subgroup where all entries are ±1 is the [[signed permutation matrices]], which is the [[hyperoctahedral group]].
* The subgroup where the entries are ''m''th [[roots of unity]] <math>\mu_m</math> is isomorphic to a [[generalized symmetric group]].
* The subgroup of diagonal matrices is [[abelian group|abelian]], normal, and a maximal abelian subgroup. The [[quotient group]] is the symmetric group, and this construction is in fact the [[Weyl group]] of the general linear group: the diagonal matrices are a [[maximal torus]] in the general linear group (and are their own [[centralizer]]), the generalized permutation matrices are the normalizer of this torus, and the quotient, <math>N(T)/Z(T) = N(T)/T \cong S_n</math> is the Weyl group.