A finite $2$-group defined by generators $x,y$ and defining relations
where $m\geq4$. The order of a quasi-dihedral group is $2^m$; the group has a cyclic invariant subgroup of index 2. The name was given because of the similarity of the defining relations with those of a dihedral group; however, a quasi-dihedral group is not isomorphic to the latter for any value of $m$. A quasi-dihedral group is sometimes called a semi-dihedral group.
|||B. Huppert, "Endliche Gruppen" , 1 , Springer (1967)|
Quasi-dihedral group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-dihedral_group&oldid=33926