If some of the people in the group are experienced, then why aren't they the ones getting the permit arranged? Does that experience include Whitney, itself, or is it general experience in the Sierra Nevada?
For a very long time up to and including about 1970, the standard way to do Whitney was as a three-day backpack trip in the months of July or August. Starting about then, some eager beavers started doing it in two days, and some of the very experienced ones started doing it as a winter trip (April-May-June). When I came along in 1976, I started doing it all in a day, but always in July or August.
Just assuming that everything else works out, permit, equipment, etc., then you really need to acclimitize for altitude before you actually start up the trail. I'm not saying that you are legally bound to. I'm just saying that if you don't, there is a very good likelihood of problems. It may be as simple as a splitting headache, or it could be much worse. The hikers who are inadequately trained and who have no previous exposure to altitude and cold have a poor success rate. I'm not saying that you are going to die, but the first experience up there is typically a lot harsher than what you expect. At a minimum, that would be two nights camped somewhere high enough that you can get some exposure to cold and wet snow where you can feel the thin air. The big risks are: hypothermia from cold wet snow, frostbitten toes from wet footware, severe sunburn, and acute mountain sickness. If you are not roped, then add some fall injury to that.