Mark FittingSubgroup and FrattiniSubgroup as nilpotent

The Frattini and Fitting subgroups of finite groups are always nilpotent.
See issue gap-system#398.

lib/grp.gi

@@ -996,13 +996,13 @@ InstallMethod( FittingSubgroup,
     "generic method for groups",
     [ IsGroup and IsFinite ],
     function (G)
-        if IsTrivial (G) then
-            return G;
-        else
-            return SubgroupNC( G, Filtered(Union( List( Set( FactorsInt( Size( G ) ) ),
+        if not IsTrivial( G ) then
+            G := SubgroupNC( G, Filtered(Union( List( Set( FactorsInt( Size( G ) ) ),
                          p -> GeneratorsOfGroup( PCore( G, p ) ) ) ),
                          p->p<>One(G)));
+            SetIsNilpotentGroup( G, true );
         fi;
+        return G;
     end);
 
 RedispatchOnCondition( FittingSubgroup, true, [IsGroup], [IsFinite], 0);
@@ -1019,7 +1019,11 @@ local m;
       return G;
     fi;
     m:=List(ConjugacyClassesMaximalSubgroups(G),C->Core(G,Representative(C)));
-    return Intersection(m);
+    m := Intersection(m);
+    if HasIsFinite(G) and IsFinite(G) then
+      SetIsNilpotentGroup(m,true);
+    fi;
+    return m;
 end);
 
 

lib/grppcatr.gi

@@ -134,7 +134,9 @@ InstallMethod( FrattiniSubgroup,
     0,
 
 function( G )
-    return Core( G, PrefrattiniSubgroup( G ) );
+    G := Core( G, PrefrattiniSubgroup( G ) );
+    SetIsNilpotentGroup( G, true );
+    return G;
 end);
 
 

lib/maxsub.gi

@@ -346,6 +346,9 @@ local m,f,i;
       f:=Core(G,NormalIntersection(f,m[i]));
     fi;
   od;
+  if HasIsFinite(G) and IsFinite(G) then
+    SetIsNilpotentGroup(f,true);
+  fi;
   return f;
 end);