Multiple Group Priveleges on same directory?


On my FTP server, I need to apply the following permissions to a directory:

1. A specific owner with full access
2. A specific group with full access
3. A specific group with read-only access
4. No access whatsoever for everyone else

I understand how to apply permission for the owner (1.), the first group (2.), and everyone else (4.)....

chown owner:group1 dirname
chmod 770 dirname

What I don't get is how to apply read only access for my second group (3.). I feel certain that I a missing something big here. Can anyone help?