"Source: Text/Group/GrpPC.text";
"Line: 2996";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 2996
// Example: H70E18 ()
print "Example: H70E18";
ei := GetEchoInput();
SetEchoInput(true);
G := DirectProduct(CyclicGroup(GrpPC,3),
                     DihedralGroup(GrpPC,3));
ns := NormalSubgroups(G);
ns;
ns[2];
N1 := ns[2]`subgroup;
N2 := ns[3]`subgroup;
c1 := Complements(G,N1);
c1;
c2 := Complements(G,N2);
c2;
Index(G,Normalizer(G,c1[1]));
assert $1 eq 1;
Index(G,Normalizer(G,c2[1]));
assert $1 eq 3;
Subgroups(G);
SetEchoInput(ei);
