Classification of rational generalized dihedral groups

Statement

Suppose $H$ is a finite abelian group with exponent $m$ and $G$ is the corresponding Generalized dihedral group (?). Then, the following are equivalent:

1. $G$ is a 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 $1,2,3,4,6$.