"Source: Text/Group/GrpPC.text";
"Line: 4652";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 4652
// Example: H70E29 ()
print "Example: H70E29";
ei := GetEchoInput();
SetEchoInput(true);
IsGoodGroup := function(G, k)
   ncl := # Classes(G);
   O := FactoredOrder(G);
   p := O[1][1];
   m := O[1][2];
   n := Floor(m / 2);
   e := m - n * 2;
   Desired := n * (p^2 - 1) + p^e + k * (p - 1) * (p^2 - 1);
   return (Desired eq ncl);
end function;
a := GeneratepGroups (3, 2, 4 : OrderBound := 5); 
#a;
assert $1 eq 42;
for i := 1 to #a do
       G := a[i];
       if IsGoodGroup(G, 0) then
          "Group ", i, " of order ", Order(G), " has abundance 0";
       end if;
end for;
SetEchoInput(ei);
