Page "Fischer group" Paragraph 8

Fischer was able to classify 3-transposition groups that satisfy certain extra technical conditions.

The groups he found fell mostly into several infinite classes ( besides symmetric groups: certain classes of symplectic, unitary, and orthogonal groups ), but he also found 3 very large new groups.

These groups are usually referred to as Fi < sub > 22 </ sub >, Fi < sub > 23 </ sub > and Fi < sub > 24 </ sub >.

The first two of these are simple groups, and the third contains the simple group Fi < sub > 24 </ sub >' of index 2.