chmod apply to user group

I need to set the permissions of a dir so that a usergroup in my ubuntu-server has read/write permissions. I understand that I’m supposed to use chmod (right?), but how do I set the permissions to only apply to a single usergroup?

chgrp $GROUPNAME $DIRNAME
chown g=$PERMS

Where $DIRNAME is the directory you want to change, $GROUPNAME is the name of the group you want the directory to be owned by, and $PERMS is the combination of rwx that you want to change permissions to.

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