"Source: Text/Group/GrpPerm.text";
"Line: 4672";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPerm.text, line: 4672
// Example: H65E27 ()
print "Example: H65E27";
ei := GetEchoInput();
SetEchoInput(true);
G := PermutationGroup< 36 | (3, 17, 26)(4, 16, 25)(5, 18, 27)(8, 15, 24),
                            (1, 32, 10)(2, 31, 11)(3, 35, 12)(6, 30, 15),
                            (12, 33, 24)(13, 29, 20)(14, 28, 19)(17, 30, 21),
                            (6, 26, 33)(7, 22, 34)(8, 21, 35)(9, 23, 36) >;
IsTransitive(G);
assert not $1;
Orbit(G, 1);
O := Orbits(G);
O;
Order(G);
assert $1 eq 933120;
f := OrbitAction(G, O[9]);
f;
Im := Image(f);
Im;
Ker := Kernel(f);
Ker;
IsElementaryAbelian(Ker);
assert $1;
SetEchoInput(ei);
