gap> ruf:=(4,2,5);
(2,5,4)
gap> rub:=(1,3,6);
(1,3,6)
gap> luf:=(3,1,8);
(1,8,3)
gap> lub:=(2,4,7);
(2,4,7)
gap> rdf:=(1,6,8);
(1,6,8)
gap> 
gap> GV:=Group(ruf,rub,luf,lub,rdf);
Group( (2,5,4), (1,3,6), (1,8,3), (2,4,7), (1,6,8) )
gap> N:=Size(GV);
144
gap> GV:=Group(ruf,rub,luf,lub,rdf,rdb,ldf,ldb);
Error, Variable: 'rdb' must have a value
gap> rdb:=(2,7,5);
(2,7,5)
gap> ldf:=(4,5,7);
(4,5,7)
gap> ldb:=(6,3,8);
(3,8,6)
gap> GV:=Group(ruf,rub,luf,lub,rdf,rdb,ldf,ldb);
Group( (2,5,4), (1,3,6), (1,8,3), (2,4,7), (1,6,8), (2,7,5), (4,5,7), 
(3,8,6) )
gap> N:=Size(GV);
144
gap> ((4*3*2)/2)^2;
144
gap> ruf0:=(4,2,5)(1,3,2);
Error, Perm: cycles must be disjoint
gap> ruf0:=(4,2,5)(10,30,20);
( 2, 5, 4)(10,30,20)
gap> rub0:=(1,3,6)(10,40,30);
( 1, 3, 6)(10,40,30)
gap> luf:=(3,1,8)(10,20,50);
( 1, 8, 3)(10,20,50)
gap> lub0:=(2,4,7)(10,50,40);
( 2, 4, 7)(10,50,40)
gap> luf0:=(3,1,8)(10,20,50);
( 1, 8, 3)(10,20,50)
gap> ldb0:=(6,3,8)(40,50,60);
( 3, 8, 6)(40,50,60)
gap> G:=Group(ruf0,rub0,luf0,lub0,ldb0);
Group( ( 2, 5, 4)(10,30,20), ( 1, 3, 6)(10,40,30), ( 1, 8, 3)(10,20,50), 
( 2, 4, 7)(10,50,40), ( 3, 8, 6)(40,50,60) )
gap> M:=Size(G);
51840
gap> (10,20,30) in G;
true
gap> (1,3)(2,4) in G;
false
gap> luf:=(3,1,8);
(1,8,3)
gap> ldf0:=(4,5,7)(20,60,50);
( 4, 5, 7)(20,60,50)
gap> rdb0:=(2,7,5)(30,40,60);
( 2, 7, 5)(30,40,60)
gap> G:=Group(ruf0,rub0,luf0,lub0,ldb0,rdb0,ldf0);
Group( ( 2, 5, 4)(10,30,20), ( 1, 3, 6)(10,40,30), ( 1, 8, 3)(10,20,50), 
( 2, 4, 7)(10,50,40), ( 3, 8, 6)(40,50,60), ( 2, 7, 5)(30,40,60), ( 4, 5, 7)
(20,60,50) )
gap> M:=Size(G);
51840
gap> (2,4,5) in G;
true
gap> quit;