Chevalley group of type F4

Definition

Let $K$ be a field.

The Chevalley group of type $F_4$ over $K$, denoted $F_4(K)$, is defined as the group corresponding to the Dynkin diagram:

File:F4Dynkindiagram.png

For a prime power $q$, $F_4(q)$ is defined as the group $F_4({\mathbb{F}}_q)$.

Arithmetic functions

Function	Value	Similar groups	Explanation
order	$q^{24}(q^{12}-1)(q^8-1)(q^6-1)(q^2-1)$

Particular cases

$q$ (field size)	$p$ (underlying prime, field characteristic)	exponent on $p$ giving $q$	Chevalley group $F_{\$}(q)$
2	2	1	Chevalley group:F4(2)
3	3	1	Chevalley group:F4(3)