FIX: RepresentativesPerfectSubgroups (#6160)

Do not just pick normal subgroups that are normal in minimal ones on top,
but their full G-orbits, with actions. This seems to avoid representative
selection issues.

Author: hulpke

lib/grplatt.gi

@@ -992,6 +992,7 @@ InstallGlobalFunction(LatticeViaRadical,function(arg)
     if Length(mpcgs)>0 then
       gf:=GF(RelativeOrders(mpcgs)[1]);
       if select=IsPerfectGroup then
+
         # the only normal subgroups are those that are normal under any
         # subgroup so far.
 
@@ -1008,7 +1009,13 @@ InstallGlobalFunction(LatticeViaRadical,function(arg)
         od;
         SortBy(nts,Size); # increasing order
         # by setting up `act' as fail, we force a different selection later
-        act:=[nts,fail];
+        #act:=[nts,fail];
+
+        # there is an issue in selecting representatives. Form G-orbits to
+        # remain in usual case.
+        nts:=Union(Orbits(G,nts));
+        act:=ActionHomomorphism(G,nts,"surjective");
+        act:=[nts,act];
 
       elif select=IsNonabelianSimpleGroup then
         # simple -> no extensions, only the trivial subgroup is valid.

tst/testbugfix/2025-11-06-perfectsubs.tst

@@ -0,0 +1,5 @@
+# missing subgroups when finding perfect subgroups
+# See <https://github.com/gap-system/gap/issues/6157>.
+gap> G:=WreathProduct(Group((1,2)), SymmetricGroup(6));;
+gap> Size(ConjugacyClassesPerfectSubgroups(G));
+8