Chevalley group of type E7

Definition

Let $K$ be a field.

The Chevalley group of type $E_{7}$ over $K$, denoted $E_{7}(K)$, is defined as the group corresponding to the Dynkin diagram:

File:E7Dynkindiagram.png

For a prime power $q$, $E_{7}(q)$ is defined as the group $E_{7}(\mathbb {F} _{q})$.

Arithmetic functions

Function	Value	Similar groups	Explanation
order	$q^{63}(q^{18}-1)(q^{14}-1)(q^{12}-1)(q^{10}-1)(q^{8}-1)(q^{6}-1)(q^{2}-1)/\operatorname {gcd} (2,q-1)$

Particular cases

$q$ (field size)	$p$ (underlying prime, field characteristic)	exponent on $p$ giving $q$	Chevalley group $E_{7}(q)$
2	2	1	Chevalley group:E7(2)
3	3	1	Chevalley group:E7(3)