The Fischer groups are three among the sporadic finite simple groups. They were discovered by Bernd Fischer in the 1970s, and are generated by a conjugacy class of involutions, the product of any two of which has order either $2$ or $3$. The group ${{Fi}_{24}}^{\'}$ is the derived subgroup (of index $2$) of a non-simple group ${\mathrm{Fi}}_{24}$ of order $2510411418381323442585600$.

The FischerGroup( n ) command returns a permutation group isomorphic to the Fischer group ${\mathrm{Fi}}_{22}$, ${\mathrm{Fi}}_{23}$ or ${{Fi}_{24}}^{\'}$ for n = 22, 23, 24, respectively.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{FischerGroup}\left(23\right)$

$G≔{Fi}_{23}$

$\mathrm{Degree}\left(G\right)$

$31671$

$\mathrm{GroupOrder}\left(G\right)$

$4089470473293004800$

$\mathrm{IsSimple}\left(G\right)$

$\mathrm{true}$

The GroupTheory[FischerGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.