gap> f1:=(1,4)(2,3); 
(1,4)(2,3)
gap> f2:=(2,5)(3,4); 
(2,5)(3,4)
gap> f3:=(3,6)(4,5); 
(3,6)(4,5)
gap> f4:=(4,7)(5,6); 
(4,7)(5,6)
gap> h1:=(1,2,3,4,5,6,7,8);
(1,2,3,4,5,6,7,8)
gap> h2:=f1*f4*f1;
(1,7)(5,6)
gap> h3:=f1*f3*f1;
(1,5)(2,6)
gap> G:=Group(h1,h2,h3);
Group( (1,2,3,4,5,6,7,8), (1,7)(5,6), (1,5)(2,6) )
gap> Size(G);
40320
gap> 8*7*6*5*4*3*2;
40320
gap> G:=Group(h1,h3);
Group( (1,2,3,4,5,6,7,8), (1,5)(2,6) )
gap> Size(G);
32
gap> IsAbelian(G);
false
gap> quit;