How do I remove one object from a group hierarchy? I don't want to delete it, just remove it from one specific group.
You can manage an object's groups from the object properties panel under the groups rollout.
These settings allow you to:
Remove the object from a specific group by clicking the x next to the group's name.
Re-name any of the groups the object belongs to by simply typing in the text box with the group's name.
Only allow the object to be visible on certain layers when duplicated (via particle system, dupli-verts, etc.) using the dupli-visibility layer selector.
Offset the object when duplicated using the x, y, z spinners.