To rotate a single group about its origin, see this.
I’m a little confused though because you’re talking about “a group”, then about “these groups”. And a (one) group in 2D has 2 components to its origin, x and y, so you can’t specify a group’s (or mesh’s) origin by just one number. In 3D that’s even 3 components: x, y, z.
Assuming you are talking of one (1) group consisting of three meshes, you’ll have to specify which point you’ll want to consider to be the center of that group.