# Finding irreducible representations of the following group using GAP

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.

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Do you know the size of the $G$? – Babak S. Mar 9 '13 at 13:49
@Unknown: I wrote the code for the $G$ in GAP. Moreover I found a link that you can find the I.R. of the $G$. Wanna that or you want a complete code? – Babak S. Mar 9 '13 at 13:57
The order of the group is 24. Thanks for asking. I will include it in the question. @sasha, thank you for the editing. – Herband Mar 9 '13 at 13:59
@BabakS., thank you very much. Yes, I would like to see the code you wrote. Can I also run it on my online sage notebook account? – Herband Mar 9 '13 at 14:01
I don't know Sage as I am familiar to the GAP. But, I add my attempt and wait to see other codes. Thanks ;-) – Babak S. Mar 9 '13 at 14:03

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);

Thanks @Babak S., I am experimenting with SAGE and I think I can use the commnad $$print gap.eval(''the gap code'')$$ to translate codes in GAP to SAGE. – Herband Mar 9 '13 at 14:15
Nice!!!!! + 1 and $\;$ 8-) – amWhy Mar 10 '13 at 4:57