Steinberg3D4 - Maple Help
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GroupTheory

 Steinberg3D4

 Calling Sequence Steinberg3D4( q )

Parameters

 q - algebraic; an algebraic expression, taken to be a prime power

Description

 • 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 ${}^{3}\mathrm{D}_{4}\left(q\right)$ .

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Steinberg3D4}\left(2\right)$
 ${G}{≔}{\mathrm{⟨a permutation group on 819 letters with 2 generators⟩}}$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${211341312}$ (2)
 > $\mathrm{Degree}\left(G\right)$
 ${819}$ (3)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsPrimitive}\left(G\right)$
 ${\mathrm{true}}$ (5)
 > $G≔\mathrm{Steinberg3D4}\left(3\right):$
 > $\mathrm{Degree}\left(G\right)$
 ${26572}$ (6)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (7)
 > $\mathrm{IsPrimitive}\left(G\right)$
 ${\mathrm{true}}$ (8)
 > $\mathrm{IsSimple}\left(\mathrm{Steinberg3D4}\left(4096\right)\right)$
 ${\mathrm{true}}$ (9)
 > $\mathrm{GroupOrder}\left(\mathrm{Steinberg3D4}\left(27\right)\right)$
 ${11956114445971661401099296184508431605312}$ (10)
 > $\mathrm{ClassNumber}\left(\mathrm{Steinberg3D4}\left(32\right)\right)$
 ${1082405}$ (11)
 > $G≔\mathrm{Steinberg3D4}\left(q\right)$
 ${G}{≔}{}^{{3}}{D}_{{4}}{}\left({q}\right)$ (12)
 > $\mathrm{ClassNumber}\left(G\right)$
 ${{q}}^{{4}}{+}{{q}}^{{3}}{+}{{q}}^{{2}}{+}{q}{+}{5}{+}{\mathrm{irem}}{}\left({q}{,}{2}\right)$ (13)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (14)

Compatibility

 • The GroupTheory[Steinberg3D4] command was introduced in Maple 2021.
 • For more information on Maple 2021 changes, see Updates in Maple 2021.