Here is a complete list of exponents for sporadic groups, produced by GAP.
[ [ "M11", 1320 ],
[ "M12", 1320 ],
[ "J1", 43890 ],
[ "M22", 9240 ],
[ "J2", 840 ],
[ "M23", 212520 ],
[ "HS", 9240 ],
[ "J3", 116280 ],
[ "M24", 212520 ],
[ "McL", 27720 ],
[ "He", 14280 ],
[ "Ru", 633360 ],
[ "Suz", 360360 ],
[ "ON", 10884720 ],
[ "Co3", 637560 ],
[ "Co2", 1275120 ],
[ "Fi22", 720720 ],
[ "HN", 2633400 ],
[ "Ly", 10651271400 ],
[ "Th", 57886920 ],
[ "Fi23", 845404560 ],
[ "Co1", 16576560 ],
[ "J4", 607938537360 ],
[ "F3+", 24516732240 ],
[ "B", 234033344344800 ],
[ "M", 1165654792878376600800 ] ]