How do I change the color of a Group?
I am assuming you mean Polygoup? If you create groups based on Polypaint the color sort of resembles the color you painted.
If you want maximum control over the colors you could create a material for each group. In your preferences>importexport if you check “Import materials as groups” you could make a colored material for each group in an external 3D app. If you use GoZ to import the file the Polygroups should all be setup with the colors from your materials.
Otherwise if you don’t care about the exact hue you could isolate your group and just repeatedly hit “group visible” until you get a color you want.