[GAP Forum] Computing conjugacy classes on matrix groups over finite fields

[Fernando Fantino]

Dear  Siddhartha,

I think that the commands:
ClassMultiplicationCoefficient
<https://www.gap-system.org/Manuals/doc/ref/chap71.html#X7E2EA9FE7D3062D3>
and
PowerMap
<https://www.gap-system.org/Manuals/doc/ref/chap73.html#X781FAA497E3B4D1A>
can help with your task.

Sincerely,
Fernando.




El lun., 27 ene. 2020 a las 8:50, Siddhartha Sarkar (<siddhartha18 at gmail.com>)
escribió:

> Dear forum,
>
> Consider the group L_3(2) which is generated by the following two matrices:
>
> X = [1,1,0; 0,1,0; 0,0,1], Y = [0,0,1; 1,0,0; 0,1,0]
>
> of order 2 and 3 whose product has order 7. Now L_3(2) has two order 7
> classes 7A and 7B.
>
> (1) Is it possible to compute in GAP in which conjugacy class the product
> XY goes to?
>
> (2) Secondly, I wish to pick an arbitrary element either from 7A or from
> 7B, look at its various powers and check whether these goes in the class
> containing XY. How is it done in GAP?
>
> I can see that the SmallGroup in GAP stores the information on conjugacy
> classes in a very different way. (I do not have access to MAGMA, by the
> way.)
>
> Regards,
> Siddhartha
> _______________________________________________
> Forum mailing list
> Forum at gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
>