Finding irreducible representations of the following group using GAP

Question

Given the following group of order 24, $$ G = \langle a,b \mid a^2=b^3=(abab^2)^2=1\rangle$$ how can one find (all) the irreducible representations using GAP? Since I have not installed GAP yet, I would like to use the SAGE interface to GAP. If you give me the SAGE code for such presentation, I will be able to compute for others too.

Thanks.

Answer 1

I think the main body of the program contains the following codes:

f:=FreeGroup(2);;

a:=f.1;; b:=f.2;;

G:=f/[a^2,b^(3),(a*b*a*b^(2))^2];;

another codes which may help us will be:

e:=Elements(s);

Size(s);

IsSolvable(s);

Now follow this link to find the exact willing: Irreducible Representations.