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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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  • $\begingroup$ Do you know the size of the $G$? $\endgroup$ – mrs Mar 9 '13 at 13:49
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    $\begingroup$ @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? $\endgroup$ – mrs Mar 9 '13 at 13:57
  • $\begingroup$ The order of the group is 24. Thanks for asking. I will include it in the question. @sasha, thank you for the editing. $\endgroup$ – Herband Mar 9 '13 at 13:59
  • $\begingroup$ @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? $\endgroup$ – Herband Mar 9 '13 at 14:01
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    $\begingroup$ I don't know Sage as I am familiar to the GAP. But, I add my attempt and wait to see other codes. Thanks ;-) $\endgroup$ – mrs Mar 9 '13 at 14:03
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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.

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  • $\begingroup$ 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. $\endgroup$ – Herband Mar 9 '13 at 14:15
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    $\begingroup$ @Herband: It is yours now. :-) Take it and see if it is work or not? $\endgroup$ – mrs Mar 9 '13 at 14:18
  • $\begingroup$ Thank you. Let me see what I can do. I will post an answer if I get it right. $\endgroup$ – Herband Mar 9 '13 at 14:24
  • $\begingroup$ Nice!!!!! + 1 and $\;$ 8-) $\endgroup$ – Namaste Mar 10 '13 at 4:57
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    $\begingroup$ hehehehehe! ;-) (Only when driving!) $\endgroup$ – Namaste Mar 10 '13 at 12:10

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