diff --git a/lib/grp.gd b/lib/grp.gd
index c40b5ab3b9..609b7581da 100644
--- a/lib/grp.gd
+++ b/lib/grp.gd
@@ -3220,7 +3220,7 @@ DeclareOperation("CentralizerModulo", [IsGroup,IsGroup,IsObject]);
 ##  <M>U_1:= <A>G</A></M>,
 ##  <M>U_i:= [<A>G</A>, U_{{i-1}}] U_{{i-1}}^{<A>p</A>}</M>.
 ##  <Example><![CDATA[
-##  gap> g:=QuaternionGroup(12);;
+##  gap> g:=DicyclicGroup(12);;
 ##  gap> PCentralSeries(g,2);
 ##  [ <pc group of size 12 with 3 generators>, Group([ y3, y*y3 ]), Group([ y*y3 ]) ]
 ##  gap> g:=SymmetricGroup(4);;
@@ -3250,7 +3250,7 @@ KeyDependentOperation( "PCentralSeries", IsGroup, IsPosInt, "prime" );
 ##  <Ref Func="PCentralSeries"/>.
 ##  <P/>
 ##  <Example><![CDATA[
-##  gap> g:=QuaternionGroup(12);;
+##  gap> g:=DicyclicGroup(12);;
 ##  gap> PRump(g,2) = PCentralSeries(g,2)[2];
 ##  true
 ##  gap> g:=SymmetricGroup(4);;
@@ -3279,7 +3279,7 @@ KeyDependentOperation( "PRump", IsGroup, IsPosInt, "prime" );
 ##  It is the core of a Sylow <A>p</A>-subgroup of <A>G</A>,
 ##  see <Ref Func="Core"/>.
 ##  <Example><![CDATA[
-##  gap> g:=QuaternionGroup(12);;
+##  gap> g:=DicyclicGroup(12);;
 ##  gap> PCore(g,2);
 ##  Group([ y3 ])
 ##  gap> PCore(g,2) = Core(g,SylowSubgroup(g,2));
diff --git a/tst/testinstall/grp/basic.tst b/tst/testinstall/grp/basic.tst
index 1cf6d3bc3f..4f85e557cd 100644
--- a/tst/testinstall/grp/basic.tst
+++ b/tst/testinstall/grp/basic.tst
@@ -225,7 +225,7 @@ Error, no method found! For debugging hints type ?Recovery from NoMethodFound
 Error, no 2nd choice method found for `DihedralGroupCons' on 2 arguments
 
 #
-# quaternion groups
+# dicyclic groups
 #
 gap> IdGroup(DicyclicGroup(4));
 [ 4, 1 ]
@@ -263,19 +263,41 @@ gap> DimensionOfMatrixGroup(G);
 
 #
 gap> DicyclicGroup(2,3);
-Error, usage: DicyclicGroup( [<filter>, [<field>, ] ]<size> )
+Error, usage: <filter> must be a filter
 gap> DicyclicGroup(IsRing,3);
-Error, no method found! For debugging hints type ?Recovery from NoMethodFound
-Error, no 1st choice method found for `DicyclicGroupCons' on 2 arguments
+Error, usage: <size> must be a positive integer divisible by 4
 gap> DicyclicGroup(0);
-Error, no method found! For debugging hints type ?Recovery from NoMethodFound
-Error, no 1st choice method found for `DicyclicGroupCons' on 2 arguments
+Error, usage: <size> must be a positive integer divisible by 4
 gap> DicyclicGroup(1);
-Error, no method found! For debugging hints type ?Recovery from NoMethodFound
-Error, no 2nd choice method found for `DicyclicGroupCons' on 2 arguments
+Error, usage: <size> must be a positive integer divisible by 4
 gap> DicyclicGroup(IsFpGroup,1);
-Error, no method found! For debugging hints type ?Recovery from NoMethodFound
-Error, no 2nd choice method found for `DicyclicGroupCons' on 2 arguments
+Error, usage: <size> must be a positive integer divisible by 4
+
+#
+# (generalised) quaternion groups
+#
+gap> QuaternionGroup(4);
+#I  Warning: QuaternionGroup called with <size> 4 which is less than 8, or not a power of 2.
+<pc group of size 4 with 2 generators>
+gap> QuaternionGroup(8);
+<pc group of size 8 with 3 generators>
+gap> QuaternionGroup(12);
+#I  Warning: QuaternionGroup called with <size> 12 which is less than 8, or not a power of 2.
+<pc group of size 12 with 3 generators>
+gap> QuaternionGroup(11);
+Error, usage: <size> must be a positive integer divisible by 4
+gap> GeneralisedQuaternionGroup(16);
+<pc group of size 16 with 4 generators>
+gap> GeneralisedQuaternionGroup(IsFpGroup, 32);
+<fp group of size 32 on the generators [ r, s ]>
+gap> GeneralisedQuaternionGroup(IsMatrixGroup, 32);
+<matrix group of size 32 with 2 generators>
+gap> F:=FunctionField(GF(16),1);;
+gap> Q:=GeneralisedQuaternionGroup(IsMatrixGroup, F, 256); 
+<matrix group of size 256 with 2 generators>
+gap> HasIsQuaternionGroup(Q);
+true
+gap> Unbind(F);; Unbind(Q);;
 
 #
 # elementary abelian groups