The Steinberg group ${}^3\mathrm{D}_4\left(q\right)$ , for a prime power $q$, is a simple group of Lie type.

The Steinberg3D4( q ) command returns a symbolic group representing the Steinberg group ${}^3\mathrm{D}_4\left(q\right)$ or, if $q=2$ or $q=3$, a permutation group isomorphic to ${}^3\mathrm{D}_4\left(q\right)$ .

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

$G≔\mathrm{Steinberg3D4}\left(2\right)$

$G≔\mathrm{\⟨a\; permutation\; group\; on\; 819\; letters\; with\; 2\; generators\⟩}$

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

$211341312$

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

$819$

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

$\mathrm{true}$

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

$\mathrm{true}$

$G≔\mathrm{Steinberg3D4}\left(3\right)\:$

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

$26572$

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

$\mathrm{true}$

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

$\mathrm{true}$

$\mathrm{IsSimple}\left(\mathrm{Steinberg3D4}\left(4096\right)\right)$

$\mathrm{true}$

$\mathrm{GroupOrder}\left(\mathrm{Steinberg3D4}\left(27\right)\right)$

$11956114445971661401099296184508431605312$

$\mathrm{ClassNumber}\left(\mathrm{Steinberg3D4}\left(32\right)\right)$

$1082405$

$G≔\mathrm{Steinberg3D4}\left(q\right)$

$G≔{}^{3}D_4\left(q\right)$

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

$q^4+q^3+q^2+q+5+\mathrm{irem}\left(q\,2\right)$

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

$\mathrm{true}$

The GroupTheory[Steinberg3D4] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.