Along with #7 (closed), we'd like to support full Lookup group integration. Ideally we'd namespace the created Google Groups so we'd have {groupid}@lookup.groups.g.apps.cam.ac.uk as the group name.
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Moving to ~"workflow::doing" as @dar17 started to look at this
To expand on the description, as this is a bit short. This is needed based on the request we have got from several users. Groups can be used to share files, folders, drives, docs, sheets, youtube videos, etc in G Suite. Lookup groups are already been used in many applications to share things across many people so it is necessary to have the same groups in G Suite, so that users can share resources with the same people.
This will also generate a single source of truth for groups and ensuring that if you update lookup group membership, this will also get updated in G Suite, avoiding having to update permissions in many places.