[GAP Forum] checking subgroups and conjugacy classes

[Nguyen,Hung Ngoc]

Dear all,

The following is beyond my GAP expertise. I appreciate very much if you can help me.

Let g:=M_{10}=A_6 . 2_3 - this is the stabilizer of a point in M_{11}. First I want to check whether g is isomorphic to a subgroup of GL(2,19). If the answer is yes, then list the structures of all groups G such that G/(C_{19} * C_{19}) = g where g acts naturally on C_{19} * C_{19}. Here C_{19} is the cyclic group of order 19.

For such a group G and a prime p dividing |G|, list the number of p-regular conjugacy classes of G (a class is p-regular if its element order is not divisible by p). 

Thank you very much,
Hung.