give permissions to a specific group of users in LDAP the same permissions as a specifc group locally in linux

Here is the problem. I have a Linux server. This server has a lot of people who need to log into it through the web server; currently authenticated by LDAP. However, I would like to allow some of the users to be able to log in locally and, more importantly, some of the users in LDAP that belong to the "administrators" LDAP group to be able to log in through ssh and be able to run commands as if they were members of the same local "administrators" group. To be clear here, there is an LDAP group called "administrators" and a local Linux group called "administrators". How do I set up my local LDAP connection so that users who log in who are members of the LDAP administrators group also authenticate as members of the local administrators group so they aren't hobbled as plebs.