"Source: Text/Group/GrpCoh.text";
"Line: 1337";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpCoh.text, line: 1337
// Example: H75E20 ()
print "Example: H75E20";
ei := GetEchoInput();
SetEchoInput(true);
G := DirectProduct(CyclicGroup(2),CyclicGroup(2));
M := TrivialModule(G,GF(2));
C := CohomologyModule(G,M);
CohomologicalDimension(C,2);
assert $1 eq 3;
D := DistinctExtensions(C);
#D;
assert $1 eq 4;
DP := [ CosetImage(g,sub<g|>) : g in D ];
[IsAbelian(d): d in DP];
[IsIsomorphic(d,DihedralGroup(4)) : d in DP];
#[g : g in DP[4] | Order(g) eq 4];
assert $1 eq 6;
SetEchoInput(ei);
