"Source: Text/Group/GrpPC.text";
"Line: 1067";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 1067
// Example: H70E6 ()
print "Example: H70E6";
ei := GetEchoInput();
SetEchoInput(true);
C4 := CyclicGroup(GrpPC,4);
E9 := AbelianGroup(GrpPC,[3,3]);
f1 := hom<E9->E9|[E9.1*E9.2^2, E9.1^2*E9.2^2]>;
f2 := hom<E9->E9|[E9.1^2,E9.2^2]>;
G := Extension(E9,C4,[f1,f2]);
G;
MR := MatrixRing(GF(3),2);
m1 := MR![1,1,1,2];
m2 := MR![2,0,0,2];
V := GModule(G,[m1,m2,Id(MR),Id(MR)]);
IsIrreducible(V);
assert $1;
v0 := V!0;
tails := [v0,v0,v0,v0,V![1,0],V![2,0],V![1,2],V![0,2],v0,V![0,1]];
H := Extension(V,G,tails);
H;
[N`order:N in NormalSubgroups(H)];
SetEchoInput(ei);
