grpfp: detect relators that are powers

lib/grpfp.gi

@@ -3790,15 +3790,26 @@ end );
 ##  enumerations with cumulatively bigger coset tables up to table size
 ##  <maxtable>. It returns `fail' if no table could be found.
 BindGlobal("FinIndexCyclicSubgroupGenerator",function(G,maxtable)
-local fgens,grels,max,gens,t,Attempt,perms,short;
+  local fgens, grels, powers, max, gens, t, Attempt, perms, short;
+
   fgens:=FreeGeneratorsOfFpGroup(G);
   grels:=RelatorsOfFpGroup(G);
+
   max:=ValueOption("max");
   if max=fail then
     max:=CosetTableDefaultMaxLimit;
   fi;
   max:=Minimum(max,maxtable);
 
+   powers := List(grels, ExtRepOfObj);
+   powers := Filtered(powers, x -> Length(x) = 2);
+   if not IsEmpty(powers) then
+     SortBy(powers, x -> x[2]);
+     if Last(powers)[2] > 10 then
+       max := Last(powers)[2];
+     fi;
+   fi;
+
   # take the generators, most frequent first
   gens:=GeneratorsOfGroup(G);
   t:=MostFrequentGeneratorFpGroup(G);