  We study the modular symmetry on magnetized toroidal orbifolds with
Scherk-Schwarz phases. In particular, we investigate finite modular flavor
groups for three-generation modes on magnetized orbifolds. The three-generation
modes can be the three-dimensional irreducible representations of covering
groups and central extended groups of $\Gamma_N$ for $N=3,4,5,7,8,16$, that is,
covering groups of $\Delta(6(N/2)^2)$ for $N=$ even and central extensions of
$PSL(2,\mathbb{Z}_{N})$ for $N=$odd. We also study anomaly behaviors.
