Also called Klein.
C2×C2 is Abelian, and is a direct product of two smaller groups.

Permutation Diagrams






C2×C2 is the rotational symmetry group of the regular maps
C2×C2 is the full symmetry group of the regular maps
Orientable  sphere  torus  2  3  4  5  6 
Nonorientable  projective plane  4  5  6  7 