diff --git a/lib/grp.gi b/lib/grp.gi
index e939bda830..f9f93651d7 100644
--- a/lib/grp.gi
+++ b/lib/grp.gi
@@ -4293,17 +4293,15 @@ InstallMethod( GroupWithGenerators,
     "generic method for collection",
     [ IsCollection ],
 function( gens )
-local G,fam,typ,id,typename;
+local G,fam,typ,id;
 
   fam:=FamilyObj(gens);
 
   typ:=IsGroup and IsAttributeStoringRep 
     and HasIsEmpty and HasGeneratorsOfMagmaWithInverses;
-  typename:="defaultGroupType";
 
   if IsFinite(gens) then
     typ:=typ and IsFinitelyGeneratedGroup;
-    typename:="defaultFinitelyGeneratedGroupType";
 
     if Length(gens)>0 and CanEasilyCompareElements(gens) then
       id:=One(gens[1]);
@@ -4311,25 +4309,15 @@ local G,fam,typ,id,typename;
         typ:=typ and HasIsTrivial and IsNonTrivial;
         if Length(gens)<=1 then
           typ:=typ and IsCyclic;
-          typename:="defaultNontrivialCyclicGroupType";
-        else
-          typename:="defaultFinitelyGeneratedNontrivialGroupType";
         fi;
       else
         typ:=typ and IsTrivial and HasIsNonTrivial;
-        typename:="defaultTrivialGroupType";
       fi;
     elif Length(gens)<=1 then
       typ:=typ and IsCyclic;
-      typename:="defaultCyclicGroupType";
     fi;
   fi;
-  if not IsBound(fam!.(typename)) then
-    typ:=NewType(fam,typ);
-    fam!.(typename):=typ;
-  else
-    typ:=fam!.(typename);
-  fi;
+  typ:=NewType(fam,typ);
 
   G:=rec();
   ObjectifyWithAttributes(G,typ,GeneratorsOfMagmaWithInverses,AsList(gens));
@@ -4341,43 +4329,31 @@ InstallMethod( GroupWithGenerators,
     "generic method for collection and identity element",
     IsCollsElms, [ IsCollection, IsMultiplicativeElementWithInverse ],
 function( gens, id )
-local G,fam,typ,typename;
+local G,fam,typ;
 
   fam:=FamilyObj(gens);
 
   typ:=IsGroup and IsAttributeStoringRep 
         and HasIsEmpty and HasGeneratorsOfMagmaWithInverses and HasOne;
-  typename:="defaultGroupWithOneType";
 
   if IsFinite(gens) then
     typ:=typ and IsFinitelyGeneratedGroup;
-    typename:="defaultFinitelyGeneratedGroupWithOneType";
 
     if Length(gens)>0 and CanEasilyCompareElements(gens) then
       if ForAny(gens,x->x<>id) then
         typ:=typ and HasIsTrivial and IsNonTrivial;
         if Length(gens)<=1 then
           typ:=typ and IsCyclic;
-          typename:="defaultNontrivialCyclicGroupWithOneType";
-        else
-          typename:="defaultNontrivialGroupWithOneType";
         fi;
       else
         typ:=typ and IsTrivial and HasIsNonTrivial;
-        typename:="defaultTrivialGroupWithOneType";
       fi;
     elif Length(gens)<=1 then
       typ:=typ and IsCyclic;
-      typename:="defaultCyclicGroupWithOneType";
     fi;
 
   fi;
-  if not IsBound(fam!.(typename)) then
-    typ:=NewType(fam,typ);
-    fam!.(typename):=typ;
-  else
-    typ:=fam!.(typename);
-  fi;
+  typ:=NewType(fam,typ);
 
   G:=rec();
   ObjectifyWithAttributes(G,typ,GeneratorsOfMagmaWithInverses,AsList(gens),
@@ -4393,15 +4369,10 @@ local G,fam,typ;
 
   fam:= CollectionsFamily( FamilyObj( id ) );
 
-  if not IsBound(fam!.defaultFinitelyGeneratedTrivialGroupWithOneType) then
-    typ:=IsGroup and IsAttributeStoringRep 
-          and HasGeneratorsOfMagmaWithInverses and HasOne and IsTrivial and
-          HasIsEmpty and HasIsNonTrivial;
-    typ:=NewType(fam,typ);
-    fam!.defaultTrivialGroupWithOneType:=typ;
-  else
-    typ:=fam!.defaultTrivialGroupWithOneType;
-  fi;
+  typ:=IsGroup and IsAttributeStoringRep 
+        and HasGeneratorsOfMagmaWithInverses and HasOne and IsTrivial and
+        HasIsEmpty and HasIsNonTrivial;
+  typ:=NewType(fam,typ);
 
   G:= rec();
   ObjectifyWithAttributes( G, typ,
diff --git a/lib/grppc.gi b/lib/grppc.gi
index d74d305d7c..66718bd8a3 100644
--- a/lib/grppc.gi
+++ b/lib/grppc.gi
@@ -347,7 +347,7 @@ InstallMethod( GroupWithGenerators,
     # override methods for `IsList' or `IsEmpty'.
     10,
 function( gens )
-local G,fam,typ,id,pcgs,typename;
+local G,fam,typ,id,pcgs;
 
   fam:=FamilyObj(gens);
   pcgs:=DefiningPcgs(ElementsFamily(fam));
@@ -357,7 +357,6 @@ local G,fam,typ,id,pcgs,typename;
     and HasIsEmpty and HasGeneratorsOfMagmaWithInverses
     and IsFinite and IsFinitelyGeneratedGroup
     and HasFamilyPcgs and HasHomePcgs and HasGeneralizedPcgs;
-  typename:="defaultFinitelyGeneratedGroupType";
 
   # we can always compare to id cheaply
   id:=One(gens[1]);
@@ -365,20 +364,11 @@ local G,fam,typ,id,pcgs,typename;
     typ:=typ and HasIsTrivial and IsNonTrivial;
     if Length(gens)<=1 then
       typ:=typ and IsCyclic;
-      typename:="defaultNontrivialCyclicGroupType";
-    else
-      typename:="defaultFinitelyGeneratedNontrivialGroupType";
     fi;
   else
     typ:=typ and IsTrivial and HasIsNonTrivial;
-    typename:="defaultTrivialGroupType";
-  fi;
-  if not IsBound(fam!.(typename)) then
-    typ:=NewType(fam,typ);
-    fam!.(typename):=typ;
-  else
-    typ:=fam!.(typename);
   fi;
+  typ:=NewType(fam,typ);
 
   G:=rec();
   ObjectifyWithAttributes(G,typ,GeneratorsOfMagmaWithInverses,AsList(gens),
@@ -396,7 +386,7 @@ InstallOtherMethod( GroupWithGenerators,
     IsMultiplicativeElementWithInverseByPolycyclicCollector] ,
     0,
 function( gens, id )
-local G,fam,typ,pcgs,typename;
+local G,fam,typ,pcgs;
 
   fam:=FamilyObj(gens);
   pcgs:=DefiningPcgs(ElementsFamily(fam));
@@ -406,27 +396,17 @@ local G,fam,typ,pcgs,typename;
         and HasIsEmpty and HasGeneratorsOfMagmaWithInverses and HasOne
         and IsFinite and IsFinitelyGeneratedGroup
         and HasFamilyPcgs and HasHomePcgs and HasGeneralizedPcgs;
-  typename:="defaultFinitelyGeneratedGroupWithOneType";
 
   # we can always compare to id cheaply
   if ForAny(gens,x->x<>id) then
     typ:=typ and HasIsTrivial and IsNonTrivial;
     if Length(gens)<=1 then
       typ:=typ and IsCyclic;
-      typename:="defaultNontrivialCyclicGroupWithOneType";
-    else
-      typename:="defaultFinitelyGeneratedNontrivialGroupWithOneType";
     fi;
   else
     typ:=typ and IsTrivial and HasIsNonTrivial;
-    typename:="defaultTrivialGroupWithOneType";
-  fi;
-  if not IsBound(fam!.(typename)) then
-    typ:=NewType(fam,typ);
-    fam!.(typename):=typ;
-  else
-    typ:=fam!.(typename);
   fi;
+  typ:=NewType(fam,typ);
 
   G:=rec();
   ObjectifyWithAttributes(G,typ,GeneratorsOfMagmaWithInverses,AsList(gens),
@@ -449,19 +429,14 @@ local G,fam,typ,pcgs;
 
   fam:= CollectionsFamily( FamilyObj( id ) );
 
-  if not IsBound(fam!.defaultFinitelyGeneratedTrivialGroupWithOneType) then
-    # pc groups are always finite and gens is finite.
-    typ:=IsGroup and IsAttributeStoringRep 
-          and HasGeneratorsOfMagmaWithInverses and HasOne
-          and IsFinite and IsFinitelyGeneratedGroup
-          and IsTrivial and HasIsNonTrivial
-          and HasIsEmpty and IsSolvableGroup
-          and HasFamilyPcgs and HasHomePcgs and HasGeneralizedPcgs;
-    typ:=NewType(fam,typ);
-    fam!.defaultTrivialGroupWithOneType:=typ;
-  else
-    typ:=fam!.defaultTrivialGroupWithOneType;
-  fi;
+  # pc groups are always finite and gens is finite.
+  typ:=IsGroup and IsAttributeStoringRep 
+        and HasGeneratorsOfMagmaWithInverses and HasOne
+        and IsFinite and IsFinitelyGeneratedGroup
+        and IsTrivial and HasIsNonTrivial
+        and HasIsEmpty and IsSolvableGroup
+        and HasFamilyPcgs and HasHomePcgs and HasGeneralizedPcgs;
+  typ:=NewType(fam,typ);
 
   pcgs:=DefiningPcgs(ElementsFamily(fam));
 
diff --git a/lib/magma.gi b/lib/magma.gi
index ed1f88f95d..19a6d2568c 100644
--- a/lib/magma.gi
+++ b/lib/magma.gi
@@ -654,14 +654,13 @@ InstallOtherMethod( MagmaWithOneByGenerators,
 #M  MagmaWithInversesByGenerators( <gens> ) . . . . . . . .  for a collection
 ##
 MakeMagmaWithInversesByFiniteGenerators:=function(family,gens)
-local M,typ,id,typename,fam;
+local M,typ,id,fam;
 
   fam:=FamilyObj(gens);
 
   typ:=IsMagmaWithInverses and IsAttributeStoringRep 
               and HasGeneratorsOfMagmaWithInverses
               and HasIsEmpty;
-  typename:="defaultMagmaWithInversesByGeneratorsType";
 
   if IsFinite(gens) then
     # typ:=typ and IsFinitelyGeneratedGroup; don't know whether group
@@ -673,19 +672,12 @@ local M,typ,id,typename,fam;
       id:=One(gens[1]);
       if ForAny(gens,x->x<>id) then
         typ:=typ and HasIsTrivial and IsNonTrivial;
-        typename:="defaultNontrivialMagmaWithInversesByGeneratorsType";
       else
         typ:=typ and IsTrivial and HasIsNonTrivial;
-        typename:="defaultTrivialMagmaWithInversesByGeneratorsType";
       fi;
     fi;
   fi;
-  if not IsBound(fam!.(typename)) then
-    typ:=NewType(fam,typ);
-    fam!.(typename):=typ;
-  else
-    typ:=fam!.(typename);
-  fi;
+  typ:=NewType(fam,typ);
 
   M:=rec();