Add html Block to show on only specific Group/Org?

Is there a way to add an HTML block to a group or organization that will show only for that specific group/org and to not show on other groups/orgs?

In my case the idea is to have each group have it's own music player on the group home page embedded on a html block but I tried doing that to a group but the html block also shows on all of the other groups. 

Thanks