Twisted or exceptional groups of Lie type are a class of finite simple groups. These are the Chevalley groups $G_2\left(q\right)$, Ree groups $R\left(q\right)$, Suzuki groups $Sz\left(q\right)$, and Steinberg-Tits triality Groups ${}^{3}D_4\left(q\right)$ where q is a power of a prime.

Note that the group $G_2\left(2\right)$is not simple, but its derived subgroup is simple (isomorphic to the simple unitary group $PSU\left(3\,3\right)$).

The ExceptionalGroup command returns a permutation group isomorphic to the exceptional group whose name is passed as argument.

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

$G≔\mathrm{ExceptionalGroup}\left(''Sz(8)''\right)$

$G≔Sz\left(8\right)$

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

$29120$

$G≔\mathrm{ExceptionalGroup}\left(''3D4(2)''\right)$

$G≔{}^{3}D_4\left(2\right)$

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

$211341312$

$G≔\mathrm{ExceptionalGroup}\left(''G2(2)''\right)$

$G≔G_2\left(2\right)$

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

$\mathrm{false}$

$L≔\mathrm{DerivedSubgroup}\left(G\right)$

$L≔\left[G_2\left(2\right)\,G_2\left(2\right)\right]$

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

$6048$

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

$\mathrm{true}$

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

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