Definition:Characterization Theorem/Historical Note

Historical Note on Characterization Theorem
If a characterization theorem does not exist for a given non-abelian finite simple group $E$, that means there may be a previously unknown simple group among the groups $G$ predicted by Upper Bound of Order of Non-Abelian Finite Simple Group.

Hence proving the non-existence of a characterization theorem such a group $E$ was a powerful technique used in the Classification of Finite Simple Groups, mainly during the $1970$s.