GroupTheory/Steinberg2E6 - Maple Help

GroupTheory

 Steinberg2E6

 Calling Sequence Steinberg2E6( q )

Parameters

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

Description

 • The Steinberg group ${}^{2}E_{6}\left(q\right)$ , for a prime power $q$, is a simple group of Lie type.
 • The Steinberg2E6( q ) command returns a symbolic group representing the Steinberg group ${}^{2}E_{6}\left(q\right)$ .

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Steinberg2E6}\left(2\right)$
 ${G}{≔}{}^{{2}}{E}_{{6}}{}\left({2}\right)$ (1)
 > $\mathrm{type}\left(G,'\mathrm{Group}'\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{type}\left(G,'\mathrm{PermutationGroup}'\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${76532479683774853939200}$ (4)
 > $\mathrm{MinPermRepDegree}\left(G\right)$
 ${3968055}$ (5)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{IsSimple}\left(\mathrm{Steinberg2E6}\left(4096\right)\right)$
 ${\mathrm{true}}$ (7)
 > $\mathrm{GroupOrder}\left(\mathrm{Steinberg2E6}\left(27\right)\right)$
 ${4423616655215750021498369285918192558448382923930662108203473523560591980763988390542885164349041907752671641600}$ (8)
 > $\mathrm{ClassNumber}\left(\mathrm{Steinberg2E6}\left(32\right)\right)$
 ${1109537246}$ (9)
 > $G≔\mathrm{Steinberg2E6}\left(q\right)$
 ${G}{≔}{}^{{2}}{E}_{{6}}{}\left({q}\right)$ (10)
 > $\mathrm{ClassNumber}\left(G\right)$
 ${{q}}^{{6}}{+}{{q}}^{{5}}{+}{2}{}{{q}}^{{4}}{+}{4}{}{{q}}^{{3}}{+}\left(\left\{\begin{array}{cc}{11}{}{{q}}^{{2}}{+}{11}{}{q}{+}{16}& {\mathrm{irem}}{}\left({q}{,}{6}\right){=}{1}\\ {12}{}{{q}}^{{2}}{+}{14}{}{q}{+}{30}& {\mathrm{irem}}{}\left({q}{,}{6}\right){=}{2}\\ {11}{}{{q}}^{{2}}{+}{11}{}{q}{+}{15}& {\mathrm{irem}}{}\left({q}{,}{6}\right){=}{3}\\ {10}{}{{q}}^{{2}}{+}{10}{}{q}{+}{14}& {\mathrm{irem}}{}\left({q}{,}{6}\right){=}{4}\\ {13}{}{{q}}^{{2}}{+}{15}{}{q}{+}{34}& {\mathrm{irem}}{}\left({q}{,}{6}\right){=}{5}\end{array}\right\\right)$ (11)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (12)
 Compatibility