Reply-To: GAP Forum <GAP-Forum@Math.RWTH-Aachen.DE>
X-Miles:        GAP Forum article 669 accepted at 22 Sep 95 12:31 +0100
Date:           22 Sep 95 14:32 +0300
From: Muradian Rudolf  <muradian@cv.jinr.dubna.su>

Dear Colleague,

Of course, the size of higher dihedral group must be larger.

But :
gap> d2 := DihedralGroup(2); Size(d2);
Group( (1,2), (3,4) )
4

gap> d4 := DihedralGroup(4); Size(d4);
Group( (1,2) )
2
Is here a bug ?

Yours, R.M.

Yes, there is a bug. (two bugs, to be more precisely).
(see the comments below)
gap> Print(DihedralPermGroup);
function ( n )
    local  D, g, h;
    if n = 2  then
        g := (1,2);
        h := (3,4);
        D := Group( g, h ); # this should be just D:=Group(g);
    else
        g := PermList( Concatenation( [ 2 .. n / 2 ], [ 1 ] ) );
        h := PermList( Concatenation( [ 1 ], Reversed( [ 2 .. n / 2 ] ) ) );
        D := Group( g, h );
        # this won't work for n=4, since D_4 cannot be (faithfully)
        # represented on 2 points.
    fi;
    return D;
endgap>

Best wishes,
Dima