LongestCoxeterElement( W )
returns the unique element of maximal length of the Coxeter group W as a permutation.
gap> LongestCoxeterElement( CoxeterGroup( "A", 4 ) );
( 1,14)( 2,13)( 3,12)( 4,11)( 5,17)( 6,16)( 7,15)( 8,19)( 9,18)(10,20)
This function requires the package "chevie" (see RequirePackage).
GAP 3.4.4