This is the unique field (up to isomorphism) having eight elements. It is denoted or . It can be defined as:
where is the field of two elements.
|Group functor||Value||GAP ID|
|additive group||elementary abelian group:E8||(8,5)|
|multiplicative group||cyclic group:Z7||(7,1)|
|general affine group of degree one||general affine group:GA(1,8)||(56,11)|
|projective special linear group of degree two||projective special linear group:PSL(3,2)||(168,42)|
The field can be defined using GAP's GF function: