[gohrt]

You can just use a 128-bit random string as a group key. That's how "private" photos are implemented on most photo sites, for example.

[dustyreagan]

I think that's the way to go for the public URLs. I'm going to leave it up to the user to come up with a unique group name though.

[benoits]

I like the flexibility, but I would suggest you add a "generate GUID" button when choosing the group name in case the user does want a random URL, which seems quite likely.