simple group of order $2^{21}.3^{16}.5^2.7^3.11.13.17.23.29 = 1255205709190661721292800 $, which is the third largest sporadic group (the two larger ones being the Baby Monster and the Monster itself). I don’t know what the rationale is behind this trinity. But I’d like to recall the (Baby)Monster history as a warning against the trinity-reflex.