You can use materials on each object in a group but not on the group as a whole.
To assign materials to objects in a group, one can select the group, in the selection palette, click the '+' sign against group to expand it, click on one of the names now exposed, and use the bottom of the selection palette to change the material, OR click the group and at the top of the selection palette, click 'edit group icon' this will allow materials to be assigned to any objects within the group as normal, click the tick icon to exit group edit mode.