Sublatum, welcome to the board as well as the wonderful hobby of hiking. You're in a great place to take advantage of some of the best hiking the US has to offer.
You'll get lots of opinions on a dayhike versus multi-day. I've done both and prefer the multi-day since you have the opportunity to enjoy yourself a little more and appreciate the scenery and surroundings longer. Hauling more weight the first and last 6 miles is the one big downside. First time Whitney hikers may find this easier overall than doing the one-day "death march".
The big thing here, though, may be the expense. If you and your friends just recently got into hiking, you may not have the gear to backpack successfully. You can spend some serious bucks on packs, sleeping bags, mattresses, stoves, cookware, filters, etc when you are keeping an eye on weight.
For training, you have peaks there in SoCal tailor-made for Whitney training - Baldy, San Jacinto and Gorgonio. Hike these peaks as often as you can. Concentrate on as much elevation gain as you can, and worry less about the mileage. You'll face 6150 feet of virtually uninterrupted uphill hiking on Whitney over 11 miles. Simulate that as much as possible and your legs will be fine for Whitney, assuming you spend time acclimating to the elevation once you're at the Portal.
The toughest part may be securing permits for a group that size. Read the "Orientation Notes for First-Timers" on this site and be sure to enter the lottery in February. If you can select weekdays for your group, versus weekends, your chance of snagging permits goes up. Be as flexible as you can with dates. If you get skunked in the lottery - likely for most of us - you go to Plan B: calling the Inyo FS office in Bishop regularly looking for cancellations. Again, flexibility with dates can reward you. Plan C is heading to Lone Pine with your group next summer and hoping for no-shows the day-of at the InterAgency Visitor Center. That can seem dicey, but it often works.
