What is the proper symmetry group of a cube in which three faces, coming together at one vertex, are painted green and the other faces are red?
I know that the axis of rotation for which the rotations of $0$, $2\pi/3$, and $4\pi/3$ produce a proper rotational group is $x=y=z$ with the intersection points being the intersection of the similarly painted faces. But I'm not sure how to formulate this into a proper symmetry group. Any help would be great, thank you in advance!