# Cayley Table of Elementary Abelian Group $E_8$

I read about elementary abelian group $$E_8$$ at https://groupprops.subwiki.org/wiki/Elementary_abelian_group:E8#Definition. I've performed some searches on other sites and have yet to come across a Cayley table for it. Any leads on where to find one?

• Why do you need such a huge ($8\times 8$) table? As long as you know the definition, you can create the Cayley table if you want. – Eclipse Sun Dec 10 '18 at 21:00
• @EclipseSun Yes, knowledge of the definition should be sufficient to generate the table. I suppose I lack supreme confidence in my execution and would like to verify. – bblohowiak Dec 11 '18 at 15:30
• I wouldn't call it E8. The usual notation is $2^3$. E8 tends to refer to a root system. – C Monsour Dec 12 '18 at 17:41

That's easy.

gap> G:=ElementaryAbelianGroup(8);;
gap> n:=8;;
gap> M:=MultiplicationTable(G);;
gap> for i in [1..n] do
> for j in [1..n] do
> Print(M[i][j]," ");
> od;
> Print("\n");
> od;
1 2 3 4 5 6 7 8
2 1 5 6 3 4 8 7
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 3 2 8 1 7 6 4
6 4 8 2 7 1 5 3
7 8 4 3 6 5 1 2
8 7 6 5 4 3 2 1