FischerGroup - Maple Help

GroupTheory

 FischerGroup

 Calling Sequence FischerGroup( n )

Parameters

 n - : {22,23,24} : integer parameter indicating the Fischer group

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{FischerGroup}\left(23\right)$
 ${G}{≔}{{Fi}}_{{23}}$ (1)
 > $\mathrm{Degree}\left(G\right)$
 ${31671}$ (2)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${4089470473293004800}$ (3)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (4)

Compatibility

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