I am traveling to San Francisco next week for two weeks and I will have my bike with me.

I am trying to find out if there are any groups that head out for an early morning 5.30 - 6am hard training ride finishing at 7 to 7.30 am? I am staying in north shore...

Mission Cycling will probably be your best bet, they're a great group of folks. Timing is close to what you're looking for, but not entirely on point.
http://missioncycling.org/rides_and_events

BTW - You may get more responses over in the Cycle Chat section, I think fewer people check in on Training.
But that's up to you whether you want to move this thread over to Cycle Chat - just ask a mod to do it.

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