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.

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

$G≔\mathrm{ChevalleyF4}\left(2\right)\:$

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

$3311126603366400$

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

$\mathrm{true}$

$G≔\mathrm{ChevalleyF4}\left(5\right)$

$G≔{\mathit{F}}_4\left(5\right)$

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

$2131486317725501953125000000000000000$

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

$\mathrm{true}$

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

$1156$

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

Error, (in GroupTheory:-Generators) cannot compute the generators of a symbolic group

$G≔\mathrm{ChevalleyF4}\left(q\right)$

$G≔{\mathit{F}}_4\left(q\right)$

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

$q^{24}\left(q^2-1\right)\left(q^6-1\right)\left(q^8-1\right)\left(q^{12}-1\right)$

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

$\mathrm{true}$

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

$\frac{\left(q^{12}-1\right)\left(q^4+1\right)}{q-1}$