#We find all primitive subgroups of $GL(4,71)$ with parameters $e=4$, $a=1$. Since in this case $b=2$ does not divide $a=1$, Lemma 5.3 implies that there exists 
#two nonconjugate subgroups $F_1$ and $F_2$ such that $N_{GL(4,71)}(F_1)/F_1\simeq O^+(4,2)$, while $N_{GL(4,71)}(F_2)/F_2\simeq O^-(4,2)$. This log-file contains
#calculations for $F_1$.
#In the notations of Theorem 5.1, if $H$ is a primitive solvable subgroup, then it possesses a series

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

#$U$ is cyclic of order $70$, $F$ is of type $2^{1+4}$ is such that $N_{GL(4,71)}(F)/F\simeq O^+(4,2)$, and $G=A=N_{GL(4,71)}(F)$. First we take the list of 
#generators of maximal solvable primitive subgroup of $GL(4,71)$, containing all maximal primitive subgroups of $GL(4,71)$ from the file   generators-GL(4,71)+.txt.

#Now we run find subgorup H generated by the set of generators gens from the file generators-GL(4,71)+.txt and check that the stabilizer of v in H is trivial, i.e.
#|v^H=|H| and Corollary 2.5 can be applied.


gap> z:=Z(71);; v:=[z,z^13,z^23,z^29];;
gap> H:=Subgroup(GL(4,71),gens);;
gap> n:=Size(H);; m:=Size(v^H);;
gap> result:=[n,n/m];
[ 80640, 1 ]