Classification of rational generalized dihedral groups

Statement
Suppose $$H$$ is a finite abelian group with exponent $$m$$ and $$G$$ is the corresponding fact about::generalized dihedral group. Then, the following are equivalent:


 * 1) $$G$$ is a fact about::rational group
 * 2) $$\varphi(m) = 1$$ or $$\varphi(m) = 2$$, where $$\varphi$$ is the Euler phi-function, counting the order of the multiplicative group of integers modulo $$m$$.
 * 3) $$m$$ is one of the numbers $$1,2,3,4,6$$.