I am trying to find representations of the group $G=GL_2(F(t)/t^2) = (M_2(F_p) , + ) \rtimes GL_n(F)$ So I was trying to do exactly what Serre has explained in this section.
I am not quite able to understand what does the following sentence mean ' systems of representativesfor the orbits of $H$ in $X$ '
ALso here what is denoted by $X/H$ ? does it correspond to quotient group ? If it is a group action then what is the action ?
I am confused.
Thanks
