Mike,
Can a group be private and unseen by the community generally,
Somewhat. But there is no equivalent to what Yahoo Groups classic called a "closed" group.
You can avoid listing the group in the Groups.io directory, and you can make your group's Messages available to members only. Also Wiki, Calendar and Guidelines; each has their own setting. But you can't make the home page itself invisible to non-members as one could in Yahoo Groups.
thus only available by invitation.
Nor can you prevent people from using the "Request Membership" button or the +subscribe email command. However, if your group has "Restricted Membership" checked you can ignore or reject all such applications.
Shal
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