FIX: IsConjugatorAutomorphism if permutation is mapped to restriction.

Also add first cheap cycle structure test to be conjugator automorphism.

This fixes #2724

lib/ghomperm.gi

@@ -1964,6 +1964,13 @@ function( hom )
 
   if IsEndoGeneralMapping( hom ) then
 
+    # cheap test for cycle structures
+    if Length(Set(List(MappingGeneratorsImages(hom),
+      x->List(x,CycleStructurePerm))))>1
+    then
+      return false;
+    fi;
+
     # test in transitive case whether we can realize in S_n
     # we do not yet compute the permutation here because we will still have to
     # test first whether it is in fact an inner automorphism:
@@ -2106,9 +2113,11 @@ function( hom )
         if rep<>fail then
           pi:=List([1..Length(orb)],x->MappingPermListList(Permuted(orb[x],rep[x]),orb[x]));
           rep:=Product(pi);
-          Assert(1,ForAll(genss,i->ImagesRepresentative(hom,i)=i^rep));
-          SetConjugatorOfConjugatorIsomorphism( hom, rep );
-          return true;
+          # must do final test, in case element maps to restricted perm
+          if ForAll(genss,i->ImagesRepresentative(hom,i)=i^rep) then
+            SetConjugatorOfConjugatorIsomorphism( hom, rep );
+            return true;
+          fi;
         fi;
 
         if ValueOption("cheap")=true then

tst/testbugfix/2018-08-22-IsConjugatorAutomorphism.tst

@@ -0,0 +1,4 @@
+gap> a:=Group((9,11)(10,12)(13,15)(14,16), (1,5,3,7)(2,6,4,8));;
+gap> hom:=GroupHomomorphismByImages(a,a,[a.1,a.2*a.1],[a.1,a.2]);;
+gap> IsConjugatorAutomorphism(hom);
+false