Quasi-dihedral group
From HandWiki
A finite $2$-group defined by generators $x,y$ and defining relations
$$x^{2^{m-1}}=y^2=x^{-1+2^{m-2}}yx^{-1}y=1,$$
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.
References
| [1] | B. Huppert, "Endliche Gruppen" , 1 , Springer (1967) |
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