x:=(24,21,20,13,19,5,23,3,18,16,6,9,22,14,4,2,17,8,15,12,7,11,10);;
y:=(4,8,9,12,10)(7,6,3,5,11)(15,19,20,23,21)(18,17,14,16,22);;
m23 := Group( x,y);
Size(m23);
#r4 := [ 0 .. 4 ];; r23 := [ 0 .. 23 ];;
#sizes := [ ];;
#for i in r23 do for j in r4 do for k in r23 do for l in r4 do
#    size := Size( Subgroup(m23, [ x^i * y^j, x^k * y^l ] ) );
#    if not size in sizes then
#       AddSet( sizes, size );
#       Print( i, "  ", j, "  ", k, "  ", l, "  ", size, "\n" );
#    fi;
#od; od; od; od;

H := Subgroup(m23, [ x^3*y^4, x^18*y^3 ] );;
Size( H );
Index( m23, H );

F2 := FreeGroup("x1","x2");
x1 := F2.1; x2 := F2.2;
#G := F2 / [(x1*x2)^2,(x1^5*x2^7)^4];
#PG := PresentationFpGroup( G );
P := PresentationViaCosetTable( m23, F2, [x1^3*x2^4,x1^18*x2^3]);