"Source: Text/Geometry/GrpPSL2.text";
"Line: 430";
"Date: Tue Jun  7 22:27:14 2016";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/GrpPSL2.text, line: 430
// Example: H142E4 ()
print "Example: H142E4";
ei := GetEchoInput();
SetEchoInput(true);
N := 34;
Chi := DirichletGroup(N, CyclotomicField(EulerPhi(N)));
GaloisConjugacyRepresentatives(Chi);
char := Chi.1^8;
G := CongruenceSubgroup([N,Conductor(char),1],char);
G;
gens := Generators(G);
#gens;
assert $1 eq 21;
g := G! [21, 4, 68, 13];
// express g in terms of Generators(G)
FindWord(G, g);
// This means that up to sign, g = gens[8]^(-1) * gens[1]
gens[8]^(-1) * gens[1];
SetEchoInput(ei);
