ChevalleyE6 - Maple Help
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GroupTheory

 ChevalleyE

 Calling Sequence ChevalleyE6( q ) ChevalleyE7( q ) ChevalleyE8( q )

Parameters

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

Description

 • The Chevalley groups ${E}_{6}\left(q\right)$ , ${E}_{7}\left(q\right)$ and ${E}_{8}\left(q\right)$ , for a prime power $q$, are exceptional simple groups of Lie type.
 • The ChevalleyE6( q ) command returns a symbolic group representing the group ${E}_{6}\left(q\right)$ .
 • The ChevalleyE7( q ) command returns a symbolic group representing the group ${E}_{7}\left(q\right)$ .
 • The ChevalleyE8( q ) command returns a symbolic group representing the group ${E}_{8}\left(q\right)$ .

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{ChevalleyE6}\left(2\right)$
 ${G}{≔}{{\mathbit{E}}}_{{6}}{}\left({2}\right)$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${214841575522005575270400}$ (2)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (3)
 > $G≔\mathrm{ChevalleyE7}\left(8\right)$
 ${G}{≔}{{\mathbit{E}}}_{{7}}{}\left({8}\right)$ (4)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${1270946186620423928101048723119547553777696702476219304626523381888123219216468469857197348448137087576946470151415398400}$ (5)
 > $\mathrm{MinPermRepDegree}\left(G\right)$
 ${2763174708875728600952247}$ (6)
 > $\mathrm{IsPerfect}\left(G\right)$
 ${\mathrm{true}}$ (7)
 > $G≔\mathrm{ChevalleyE8}\left(3\right)$
 ${G}{≔}{{\mathbit{E}}}_{{8}}{}\left({3}\right)$ (8)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${18830052912953932311099032439972660332140886784940152038522449391826616580150109878711243949982163694448626420940800000}$ (9)
 > $\mathrm{ClassNumber}\left(G\right)$
 ${12825}$ (10)
 > $\mathrm{IsSoluble}\left(G\right)$
 ${\mathrm{false}}$ (11)

Compatibility

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