GroupTheory/ChevalleyF4 - Maple Help

GroupTheory

 ChevalleyF4

 Calling Sequence ChevalleyF4( q )

Parameters

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

Description

 • The Chevalley group ${F}_{4}\left(q\right)$ , for a prime power $q$, is a simple group of Lie type.
 • The ChevalleyF4( q ) command returns a permutation group isomorphic to the Chevalley group ${F}_{4}\left(q\right)$ , for $q=2$. For non-numeric values of the argument q, or for prime powers $q$ larger than $2$, a symbolic group representing the group ${F}_{4}\left(q\right)$ is returned.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{ChevalleyF4}\left(2\right):$
 > $\mathrm{GroupOrder}\left(G\right)$
 ${3311126603366400}$ (1)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (2)

If the value of the prime power $q$ is too large, or if $q$ is a non-numeric expression, then a symbolic group representing ${F}_{4}\left(q\right)$ is returned.

 > $G≔\mathrm{ChevalleyF4}\left(5\right)$
 ${G}{≔}{{\mathbit{F}}}_{{4}}{}\left({5}\right)$ (3)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${2131486317725501953125000000000000000}$ (4)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{ClassNumber}\left(G\right)$
 ${1156}$ (6)
 > $\mathrm{Generators}\left(G\right)$
 > $G≔\mathrm{ChevalleyF4}\left(q\right)$
 ${G}{≔}{{\mathbit{F}}}_{{4}}{}\left({q}\right)$ (7)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${{q}}^{{24}}{}\left({{q}}^{{2}}{-}{1}\right){}\left({{q}}^{{6}}{-}{1}\right){}\left({{q}}^{{8}}{-}{1}\right){}\left({{q}}^{{12}}{-}{1}\right)$ (8)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (9)
 > $\mathrm{MinPermRepDegree}\left(G\right)$
 $\frac{\left({{q}}^{{12}}{-}{1}\right){}\left({{q}}^{{4}}{+}{1}\right)}{{q}{-}{1}}$ (10)
 Compatibility