How bizarre!
I was JUST pricing LAX-SFO, Aug 21 depart #1936, Aug 22 return #1931 and found a G fare (GE7DNR) - and I've never seen it before either.
On AA.com it's in the deeply discounted group with Q,N and S - but I've look at AA.com's Elite Requirement page like 2 days ago and I could swear at that time there wasn't a "G".
(BTW - The fare for the above flights is $200 - hardly a bargain).