 Generalized dihedral group

For an abelian group $A$, the generalized dihedral group is the semidirect product $A⋊C_2$ in which the nonidentity element of $C_2$ acts on $A$ by inversion.

The Generalized Dihedral Group, often denoted \( \text{GD}(n) \) or \( D_n^* \), is a group that generalizes the properties of the traditional dihedral group. The dihedral group \( D_n \) is the group of symmetries of a regular polygon with \( n \) sides, and it includes both rotations and reflections. It has the order \( 2n \) (i.e.