"Source: Text/Group/Grp.text";
"Line: 1658";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/Grp.text, line: 1658
// Example: H64E13 ()
print "Example: H64E13";
ei := GetEchoInput();
SetEchoInput(true);
G<a, b> := Group< a, b | a^3, b^3, (b * a)^4,
    ((b^-1)^a * b^-1)^2 * b^a * b >;
Order(G);
assert $1 eq 168;
H := sub< G | a^2 * b^2, (a * b)^2 >;
Index(G, H);
assert $1 eq 7;
f, L := CosetAction(G, H);   
f;
L;
Order(L);
assert $1 eq 168;
SetEchoInput(ei);
