Er yes, Tits group T is not a sporadic according to the usual accounting, I just was following the ATLAS web pages like a monkey and those guys are a gazillion times more expert than I am. Anyhow, if my search thru the ATLAS to find out which simple groups have outer auts, is not to be largely a waste of time, then we need next to answer: when simple groups are glued together to make more complex groups, what happens to the count of their outer automorphisms? If you understood that and understood simples, then you'd understand everything about finite groups (at least as far as the question of their outer auts was concerned, which may or may not in turn provide answer to Asimov). At least if you believe in the Group Classification Theorem [which seems largely unverifiable by those of us who want to do anything else in their lives]. There might be no simple and complete answer to this follow-up question, though -- but probably at least partial answers can be got. Indeed, I've never even seen any simple answer to the question: "how, exactly, are simple groups glued together to build all other finite groups?" These gluings can sometimes be very messy and hard to be confident you've really found them all.