Improvements to factor permutation code

Allow degree up to 100000 (computers are bigger now) before hard
Use maximal subgroups in trying perm rep.

(Do not use maxsub in factor if called from maxsub)

lib/factgrp.gi

@@ -545,7 +545,7 @@ end);
 BADINDEX:=1000; # the index that is too big
 GenericFindActionKernel:=function(arg)
 local G, N, knowi, goodi, simple, uc, zen, cnt, pool, ise, v, bv, badi,
-totalcnt, interupt, u, nu, cor, zzz,bigperm,perm,badcores;
+totalcnt, interupt, u, nu, cor, zzz,bigperm,perm,badcores,max,i;
 
   G:=arg[1];
   N:=arg[2];
@@ -657,7 +657,7 @@ totalcnt, interupt, u, nu, cor, zzz,bigperm,perm,badcores;
 	fi;
 	totalcnt:=totalcnt+1;
 	if KnownNaturalHomomorphismsPool(G,N) and
-	  Minimum(Index(G,v),knowi)<20000 
+	  Minimum(Index(G,v),knowi)<100000 
 	     and 5*totalcnt>Minimum(Index(G,v),knowi,1000) then
 	  # interupt if we're already quite good
 	  interupt:=true;
@@ -695,7 +695,7 @@ totalcnt, interupt, u, nu, cor, zzz,bigperm,perm,badcores;
       if Size(cor)>Size(N) and IsSubset(cor,N) and not cor in badcores then
 	Add(badcores,cor);
       fi;
-      # store known information(we do't act, just store the subgroup.
+      # store known information(we do't act, just store the subgroup).
       # Thus this is fairly cheap
       pool.dotriv:=true;
       zzz:=AddNaturalHomomorphismsPool(G,cor,u,Index(G,u));
@@ -708,6 +708,17 @@ totalcnt, interupt, u, nu, cor, zzz,bigperm,perm,badcores;
       zzz:=DegreeNaturalHomomorphismsPool(G,N);
 
       Info(InfoFactor,3,"  ext ",cnt,": ",Index(G,u)," best degree:",zzz);
+      if Size(cor)>Size(N) and Index(G,u)*2<knowi and
+      ValueOption("inmax")=fail then
+        max:=Filtered(MaximalSubgroupClassReps(u),
+	  x->IndexNC(G,x)<knowi and IsSubset(x,N)); 
+        for i in max do
+	  cor:=Core(G,i);
+	  AddNaturalHomomorphismsPool(G,cor,i,Index(G,i));
+	od;
+	zzz:=DegreeNaturalHomomorphismsPool(G,N);
+	Info(InfoFactor,3,"  Maxes: ",Length(max)," best degree:",zzz);
+      fi;
     else
       zzz:=DegreeNaturalHomomorphismsPool(G,N);
     fi;

lib/maxsub.gi

@@ -394,7 +394,7 @@ end);
 # here in case the generic normalizer code is still missing improvements
 BindGlobal("MaxesCalcNormalizer",function(P,U)
 local map, s, b, bl, bb, sp;
-  map:=SmallerDegreePermutationRepresentation(P);
+  map:=SmallerDegreePermutationRepresentation(P:inmax);
   if Range(map)=P then
     map:=fail;
   else