In the long process that resulted in the classification of finite simple groups, some of the exceptional groups were only shown to exist after people had computed (most of) their character tables and other such precise information which usually can only be attached to things that exist. Maybe someone familiar with the details can tell me/us:
Was there at some point a finite simple group conjectured to exist that turned out not to exist in the end?
If so, this part of the story is much less told than the successful part! It would be interesting to know if for such a non-existent group, say, the character table was computed, and so on...
I am asking because I just read this question on Math.SE and it reminded me I have always wanted to know this.