A Group of Order 8,315,553,613,086,720,000 by J H Conway, Bull. London Math. Soc. (1969) 1 (1): 79-88, http://blms.oxfordjournals.org/content/1/1/79.extract
Maybe it's cheating to call this memorable - I remembered there was a Conway paper with a title of this type, but I certainly don't claim to have remembered the exact title!