Group that is hidden from public but requires no membership

I would like to create a group that is:

  • NOT on my main navigation
  • does NOT present if someone were to search for it
  • only accessible if I provide them the link such as in an email.
  • I also do not want the members to have to register for the group.
  • I do not want Google to index/crawl the group

If I place the group as a public group then all content that is in that group would be found by anyone in the main search options.  If I place the group as a private then would need to deal with membership-- unless there is a way to make the private group auto accept anyone that came to that group.

Could I create a specific permission for that group?

How could I go about doing this?