[GAP Forum] Cohomology computations, ExtensionRepresentatives: possible bug

[Vipul Naik]

I am using GAP's CompatiblePairs and ExtensionRepresentatives
functions to find the orbits on the second cohomology group (set of
extensions) H^2(G;A) under the action of Aut(G) X Aut(A) for the
trivial G-action of A. This works perfectly fine for most groups G and
A, giving results that agree with my own calculations. However, for one particular pair of groups, it gives the wrong answer:

gap> G := CyclicGroup(4);;
gap> A := TrivialGModule(G,GF(2));;
gap> A1 := AutomorphismGroup(G);;
gap> A2 := GL(1,2);;
gap> D := DirectProduct(A1,A2);;
gap> P := CompatiblePairs(G,A,D);;
gap> M := ExtensionRepresentatives(G,A,P);;
gap> List(M,IdGroup);
[ [ 8, 2 ], [ 8, 2 ] ]

The answer I expect is [8,1] and [8,2].

Just printing out extensions works fine:

gap> G := CyclicGroup(4);;
gap> A := TrivialGModule(G,GF(2));;
gap> L := Extensions(G,A);;
gap> List(L,IdGroup);
[ [ 8, 2 ], [ 8, 1 ] ]

The ExtensionRepresentatives works well for most other pairs I tested
it with; I have appended some calculations to show this.

Anybody have an idea if this is the result of a bug in the GAP code,
or am I making some mistake in using the code?

Vipul

PS: Some calculations to show that ExtensionRepresentatives works well
in most cases:

For cyclic group of order 2 on cyclic group of order 2:

gap> G := CyclicGroup(2);;
gap> A := TrivialGModule(G,GF(2));;
gap> A1 := AutomorphismGroup(G);;
gap> A2 := GL(1,2);;
gap> D := DirectProduct(A1,A2);;
gap> P := CompatiblePairs(G,A,D);;
gap> M := ExtensionRepresentatives(G,A,P);;
gap> List(M,IdGroup);
[ [ 4, 2 ], [ 4, 1 ] ]

For Klein four-group on cyclic group of order 2:

gap> G := ElementaryAbelianGroup(4);;
gap> A := TrivialGModule(G,GF(2));;
gap> A1 := AutomorphismGroup(G);;
gap> A2 := GL(1,2);;
gap> D := DirectProduct(A1,A2);;
gap> P := CompatiblePairs(G,A,D);
gap> M := ExtensionRepresentatives(G,A,P);;
gap> List(M,IdGroup);
[ [ 8, 5 ], [ 8, 2 ], [ 8, 3 ], [ 8, 4 ] ]