#We find all primitive subgroups of $GL(9,7)$ with parameters $e=9$, $a=1$
#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 $12$, $F=U\circ E$ and $E$ is extraspecial of order $2^{1+6}$, in this case $H=A$. 

#First we make general variables:

gap> e:=8;; p:=13;; d:=8;; a:=1;;
gap> z:=Z(13);;
gap> v:=[z,z^5,z^7,0*z,z^11,z^2,z,z^3];;
gap> result:=[];

#Now we run the following loop, where gens is the list of generators from generators-GL(8,13).txt. Each entry of the list result has three items: the first is the
#number of the group in the list gens, the second is the order of the group, and the third is the order of the stabilizer of v in H. 
#If the order of the stabilizer is 1, then |v^H=|H| and Corollary 2.5 can be applied.


gap> for k in [1..Size(gens)] do
> H:=Subgroup(GL(8,13),gens[k]);;
> n:=Size(H);;
> m:=Size(v^H);
> result[k]:=[k,n,n/m];
> Display(result[k]);
> od;
[ 1, 6912, 1 ]
[ 2, 6912, 1 ]
[ 3, 10752, 1 ]
[ 4, 11520, 1 ]
[ 5, 13824, 1 ]
[ 6, 13824, 1 ]
[ 7, 13824, 1 ]
[ 8, 13824, 1 ]
[ 9, 20736, 1 ]
[ 10, 20736, 1 ]
[ 11, 20736, 1 ]
[ 12, 23040, 1 ]
[ 13, 23040, 1 ]
[ 14, 23040, 1 ]
[ 15, 32256, 1 ]
[ 16, 27648, 1 ]
[ 17, 41472, 1 ]
[ 18, 41472, 1 ]
[ 19, 41472, 1 ]
[ 20, 41472, 1 ]
[ 21, 41472, 1 ]
[ 22, 41472, 1 ]
[ 23, 41472, 1 ]
[ 24, 41472, 1 ]
[ 25, 46080, 1 ]
[ 26, 46080, 1 ]
[ 27, 46080, 1 ]
[ 28, 62208, 1 ]
[ 29, 82944, 1 ]
[ 30, 82944, 1 ]
[ 31, 82944, 1 ]
[ 32, 82944, 1 ]
[ 33, 82944, 1 ]
[ 34, 82944, 1 ]
[ 35, 82944, 1 ]
[ 36, 82944, 1 ]
[ 37, 82944, 1 ]
[ 38, 82944, 1 ]
[ 39, 82944, 1 ]
[ 40, 92160, 1 ]
[ 41, 124416, 1 ]
[ 42, 124416, 1 ]
[ 43, 124416, 1 ]
[ 44, 165888, 1 ]
[ 45, 165888, 1 ]
[ 46, 165888, 1 ]
[ 47, 165888, 1 ]
[ 48, 165888, 1 ]
[ 49, 165888, 1 ]
[ 50, 165888, 1 ]
[ 51, 165888, 1 ]
[ 52, 165888, 1 ]
[ 53, 165888, 1 ]
[ 54, 248832, 1 ]
[ 55, 248832, 1 ]
[ 56, 331776, 1 ]
[ 57, 331776, 1 ]
[ 58, 497664, 1 ]
[ 59, 497664, 1 ]
[ 60, 497664, 1 ]
[ 61, 497664, 1 ]
[ 62, 995328, 1 ]
[ 63, 995328, 1 ]