load "Subgroups/functions.txt";

G:=ChevalleyGroup("G",2,3);
IrrAll:=IrreducibleModules(G,GF(3));
G:=Group(IrrAll[1]);
Irr:=[IrrAll[i]:i in [1,2,3,6]];
labs:=["1","7_1","7_2","49"];

// We are just looking at Case 4.

A1:=Irr[4];
for i in [2,1,3,2,3] do E,rho:=Ext(A1,Irr[i]); A1:=MaximalExtension(A1,Irr[i],E,rho); DescribeLayers(Dual(A1),Irr,labs); end for;
for i in [1,2] do Dimension(Ext(A1,Irr[i])) eq 0; end for;
for i in [4,1] do E,rho:=Ext(A1,Irr[i]); A1:=MaximalExtension(A1,Irr[i],E,rho); DescribeLayers(Dual(A1),Irr,labs); end for;
Dimension(Socle(A1)) lt 7;

A2:=SocleSeries(Dual(A1))[5];
A2:=RemoveFromTop(A2,Irr,Irr,[2,3,4]);
Multiplicity(IdentifyFactors(A2,Irr),1) eq Dimension(AHom(A2,Irr[1]));

A3:=Dual(SocleSeries(A1)[2]);
for i in IndecomposableSummands(A3) do DescribeLayers(i,Irr,labs); end for;











