What is "sporadic group"

n. (context group theory English) any one of the 26 (l en exceptional) (l en finite) (l en simple group simple groups), which do not belong to any of the general, infinite categories specified in the (l en classification) (l en theorem)

In group theory, a discipline within mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups.

A simple group is a group G that does not have any normal subgroups except for the trivial group and G itself. The classification theorem states that the list of finite simple groups consists of 18 countably infinite families, plus 26 exceptions that do not follow such a systematic pattern. These are the sporadic groups. They are also known as the sporadic simple groups, or the sporadic finite groups. Because it is not strictly a group of Lie type, the Tits group is sometimes regarded as a sporadic group, in which case the sporadic groups number 27.

The monster group is the largest of the sporadic groups and contains all but six of the other sporadic groups as subgroups or subquotients.