The ability to mention groups ios not currently supported, you should cast your vote to https://jira.atlassian.com/browse/JRA-28225if you wish to see it implemented.
The "Share" feature does not support groups either, but does support emails.
We solved the problem by creating a fake system account with a Distribution List for out team as the email. But the new ability (JIRA 5?) to just free-ty[pe emails eliminates the need for a fake user.
Maybe this free plugin would be a nice work around solution for your request?
You will be able to share filter list or single issues to external users. These plugin generate a unique link, that you can share to everyone you like
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