The Fischer groups are the three sporadic groups 
, 
, and 
. These groups were discovered during the investigation
of 3-transposition groups.
The Fischer groups are implemented in the Wolfram Language as FischerGroupFi22[], FischerGroupFi23[], and FischerGroupFi24Prime[].
The following table summarizes the orders of the Fischer groups.
| group | order | factorization |
 | 64561751654400 |  |
 | 4089470473293004800 |  |
 | 1255205709190661721292800 |  |
The baby monster group is sometimes called Fischer's baby monster group.
