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 $E_8\left(q\right)$ .

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

$G≔\mathrm{ChevalleyE6}\left(2\right)$

$G≔{\mathit{E}}_6\left(2\right)$

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

$214841575522005575270400$

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

$\mathrm{true}$

$G≔\mathrm{ChevalleyE7}\left(8\right)$

$G≔{\mathit{E}}_7\left(8\right)$

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

$1270946186620423928101048723119547553777696702476219304626523381888123219216468469857197348448137087576946470151415398400$

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

$2763174708875728600952247$

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

$\mathrm{true}$

$G≔\mathrm{ChevalleyE8}\left(3\right)$

$G≔{\mathit{E}}_8\left(3\right)$

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

$18830052912953932311099032439972660332140886784940152038522449391826616580150109878711243949982163694448626420940800000$

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

$12825$

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

$\mathrm{false}$

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

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