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

[Siddhartha Sarkar]

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