Looks like this is one of those longstanding feature requests, linked above. It would seem the best that can be done currently is to rely on group names, but these aren't editable and therefore potentially obsolete. If there's doubt about whether a certain user is part of a group, the user's groups can be viewed on their JIRA profile, but you'll only see groups of which you're also a member, as described here. (A user may be a member of other groups that you don't have permission to know about.)
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