Generate a group with Cyclotomic representation in GAP

Question

I am trying to create a matrix group in GAP, but I am having problems because "it runs out of memory". The group in question is related to GL(2,3).

The problem is that I do not know if I am representing in the correct form the Cyclotomic numbers.

So, GAP manual says that the way to use this number is E(n): $e_n = \text{exp}(2π i/n)$, and my matrix elements have the form $$\frac{1}{2}\left[exp\left(\frac{2\,i\pi}{8}\right)-exp\left(\frac{2\,i\pi\,3}{8}\right)\right]$$ I am using the form

(1/2)*(E(8)-E(8)^3)

Using this form, I try to generate all the 48 elements of the group, as

g:=[[(1/2)*(E(8)-E(8)^3),(1/2)*(E(3)-E(8)^3)],
    [(1/2)*(E(8)-E(8)^3),(1/2)*(-E(8)+E(8)^3)]];
h:=[[E(8)^3,0],[0,E(8)]];

G:=Group(g,h);

and the elements:

Elements(G);

the problem is that at the end I obtain the error

gap: cannot extend the workspace any more!

Evidently, I am doing something wrong but I am not sure what. I am new In GAP and group theory, so I am not sure what is happening. Does anybody has a clue? Thanks in advance.

Answer 1

[Just to have the question answered:]

The problem will go away once typing mistakes have been fixed.