"Source: Text/Group/GrpPC.text";
"Line: 1706";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 1706
// Example: H70E10 ()
print "Example: H70E10";
ei := GetEchoInput();
SetEchoInput(true);
G := DihedralGroup(GrpPC,4);
num_map := NumberingMap(G);
for x in G do
  print x,"->",num_map(x);
end for;
6 @@ num_map;
G1 := SmallGroup(3^6, 60);
G2 := SmallGroup(3^6, 392);
function hist(G, trials)
  // Given a 3-group G, of exponent <= 3^5,
  // return a sequence whose ith term is the
  // number of elements of order p^(i-1) out
  // of trials randomly chosen elements.
  table := [0,0,0,0,0,0];
  for i := 1 to trials do
    x := Random(G);
    n := Ilog(3, Order(x));
    table[n+1] +:= 1;
  end for;
  return table;
end function;
t1 := hist(G1,100);
t1;
t2 := hist(G2,100);
t2;
for e in t1 do print ":","@"^e; end for;
for e in t1 do print ":","@"^e; end for;
SetEchoInput(ei);
