Sporadic Group

In the mathematical field of group theory, a sporadic group is one of the 26 exceptional groups in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the subgroup consisting only of the identity element, 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. Sometimes (such as by John Conway) the Tits group is regarded as a sporadic group (because it is not strictly a group of Lie type), in which case there are 27 sporadic groups.

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