G:=PrimitiveGroup(100,3);
module:=PermutationGModule(G,GF(2));
bsm:=MTX.BasesSubmodules(module);
sm:=List(bsm,bas->Submodule(GF(2)^100,bas));;
for i in [1..Length(bsm)] do
Print(Dimension(sm[i])," ");
for j in [1..i] do
if IsSubspace(sm[i],sm[j]) then Print(" 1 ");
else Print(" . ");
fi;
od;
Print("\n");
od;
mod21:=MTX.InducedActionSubmodule(module,bsm[3]);
b2:=List(bsm[2],x->Coefficients(Basis(sm[3],bsm[3]),x);;
b2:=List(bsm[2],x->Coefficients(Basis(sm[3],bsm[3]),x));;
mod20a:=MTX.InducedActionFactorModule(mod21,b2);;
MTX.IsAbsolutelyIrreducible(mod20a);
mod77:=MTX.InducedActionSubmodule(module,bsm[7]);;
b3:=List(bsm[3],x->Coefficients(Basis(sm[7],bsm[7]),x));;
mod56:=MTX.InducedActionFactorModule(mod77,b3);;
MTX.IsAbsolutelyIrreducible(mod56);
gap> W:=Subspace(GF(2)^100,bsm[3]);
d:=DistancesDistributionMatFFEVecFFE(bsm[3],GF(2),0*bsm[3][1]);
Position(d,3850);
W:=Subspace(GF(2)^100,bsm[3]);
repeat
w:=Random(W);
until WeightVecFFE(w) =32;
w;
Gmat:=Group(MTX.Generators(module));
orbit:=Orbit(Gmat,w,OnRight);;
Length(orbit);
Gper:=Image(ActionHomomorphism(Gmat,orbit));
IsPrimitive(Gper);
U:=Stabilizer(Gper,1);
U:=Image(SmallerDegreePermutationRepresentation(U));
DegreeOperation(U);
nsU:=NormalSubgroups(U);
IsElementaryAbelian(nsU[2]);
FactorGroup(U,nsU[2]);
Size(last);
720
a:=AllPrimitiveGroups(DegreeOperation,24);
m24:=last[1];
Size(m24);
G:=m24;
module:=PermutationGModule(G,GF(2));
W:=Subspace(GF(2)^24,bsm[3]);
DistancesDistributionMatFFEVecFFE(bsm[3],GF(2),0*bsm[3][1]);
[ 1, 0, 0, 0, 0, 0, 0, 0, 759, 0, 0, 0, 2576, 0, 0, 0, 759, 0, 0, 0, 0, 0, 0, 
  0, 1 ]
Position(last,759);
repeat
w:=Random(W);
until WeightVecFFE(w) =8;
w;
Gmat:=Group(MTX.Generators(module));
orbit:=Orbit(Gmat,w,OnRight);;
Length(orbit);
759