#We find all primitive subgroups of $GL(6,2)$ with parameters $e=3$, $a=2$
#In the notations of Theorem 5.1, if $H$ is a primitive solvable subgroup, then it possesses a series

#$$1<U<F<A<H,$$

#where $U$ is cyclic of order $17^2-1$, $F=U\circ E$ and $E$ is extraspecial of order $3^{1+2}$, moreover
#in this case $|H:A|$ divides $2$.

#We take the generators as a list gens from the file generators-GL(6,17).txt, choose a vector v, and check that |H|=|v^H| so that Corollary 2.5 can be applied.

gap> H:=Subgroup(GL(6,17),gens);;
gap> n:=Size(H);;
gap> z:=Z(17);; v:=[z,z^3,z^5,z^7,z^9,0*z];;
gap> m:=Size(v^G);; n/m;
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