"Source: Text/Group/GrpASim.text";
"Line: 3808";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpASim.text, line: 3808
// Example: H72E20 ()
print "Example: H72E20";
ei := GetEchoInput();
SetEchoInput(true);
//no-test [takes too much memory]
q := 2^121;
G := Sz(q);
G ^:= Random(Generic(G));
G := DerivedGroupMonteCarlo(G);
NumberOfGenerators(G);
time SuzukiRecognition(G);
time flag, iso, inv, g2slp, slp2g := RecogniseSz(G);
R := RandomProcess(G);
g := Random(R);
time w := Function(g2slp)(g);
// evaluating SLPs always takes some time
time slp2g(w) eq g;
assert $1;
p := Random([x[1] : x in Factorization(q - 1)]);
time R := SuzukiSylow(G, p);
time S := SuzukiSylow(G, p);
// that was easy, as is conjugating them
time g, slp := SuzukiSylowConjugacy(G, R, S, p);
slp2g(slp) eq g;
assert $1;
#R, NumberOfGenerators(R);
time R := SuzukiSylow(G, 2);
time S := SuzukiSylow(G, 2);
NumberOfGenerators(R), #R;
time g, slp := SuzukiSylowConjugacy(G, R, S, 2);
SetEchoInput(ei);
