diff --git a/experimental/GModule/Brueckner.jl b/experimental/GModule/Brueckner.jl
index b943de1edbd8..808145e05a3f 100644
--- a/experimental/GModule/Brueckner.jl
+++ b/experimental/GModule/Brueckner.jl
@@ -29,6 +29,10 @@ Note: the reps are NOT necessarily over the smallest field.
 
 Note: the field is NOT extended - but it throws an error if it was too small.
 
+Note: `group(M)` for the returned gmodules `M` will have a pcgs of `G` as
+      its `gens` value, thus these generators will in general differ from
+      the generators of `G`.
+
 Implements: Brueckner, Chap 1.2.3
 """
 function reps(K, G::Oscar.GAPGroup)
@@ -91,7 +95,7 @@ function reps(K, G::Oscar.GAPGroup)
           # xX for x in the field., hence Xp = X^p is defined up
           # to p-th powers: x^p Xp, so
           # C x^p Xp = Y
-          # appliying det:
+          # applying det:
           # det(C x^p Xp) = C^n x^(pn) det(Xp) = det(Y) = root-of-1
           # so I think that shows that C is (up to p-th powers)
           # also a root-of-1
@@ -114,7 +118,7 @@ function reps(K, G::Oscar.GAPGroup)
           z[1:n,(p-1)*n+1:end] = Y
           #= This is wrong in Brueckner - or he's using a different
              conjugation. Max figured out what to do: the identity block
-             needs to be lower left, and ubbber right the inverse.
+             needs to be lower left, and upper right the inverse.
 
              He might have been doing other conjugations s.w.
           =#
diff --git a/experimental/GModule/Cohomology.jl b/experimental/GModule/Cohomology.jl
index aa32aae0ae39..75d4548d7c0f 100644
--- a/experimental/GModule/Cohomology.jl
+++ b/experimental/GModule/Cohomology.jl
@@ -90,6 +90,7 @@ Base.hash(a::MultGrpElem, u::UInt = UInt(1235)) = hash(a.data. u)
     r.ac = ac
     r.M = M
     @assert all(x -> domain(x) == codomain(x) == r.M, ac)
+    @assert length(ac) == number_of_generators(G)
     @hassert :GroupCohomology 1 is_consistent(r)
     return r
   end
diff --git a/experimental/GModule/test/runtests.jl b/experimental/GModule/test/runtests.jl
index c379e59525ff..d688fae66d2c 100644
--- a/experimental/GModule/test/runtests.jl
+++ b/experimental/GModule/test/runtests.jl
@@ -57,20 +57,13 @@ end
   L = [
           matrix(F, [0 0 1; 1 0 0; 0 1 0]),
           matrix(F, [2 0 0; 0 1 0; 0 0 2]),
-          matrix(F, [2 0 0; 0 2 0; 0 0 1]),
-          matrix(F, [1 0 0; 0 1 0; 0 0 1])
       ]
   m = free_module(F, 3)
   M = GModule(m, G, [hom(m, m, a) for a in L])
 
   E = GF(3,6)
   phi = embed(F, E)
-  LE = [
-          matrix(E, [0 0 1; 1 0 0; 0 1 0]),
-          matrix(E, [2 0 0; 0 1 0; 0 0 2]),
-          matrix(E, [2 0 0; 0 2 0; 0 0 1]),
-          matrix(E, [1 0 0; 0 1 0; 0 0 1])
-      ]
+  LE = [map_entries(phi, x) for x in L]
   mE = free_module(E, 3)
 
   @test extension_of_scalars(M, phi) == GModule(mE, G, [hom(mE, mE, a) for a in LE])