gap> 
gap> ruf:=(1,11,17)(2,12,20)(4,10,18)(22,6,14)(25,27,29);
( 1,11,17)( 2,12,20)( 4,10,18)( 6,14,22)(25,27,29)
gap> rub:=(2,10,22)(1,9,23)(3,11,21)(17,5,15)(25,27,30);
( 1, 9,23)( 2,10,22)( 3,11,21)( 5,15,17)(25,27,30)
gap> luf:=(6,12,18)(5,11,19)(7,9,17)(21,1,13)(26,27,29);
( 1,13,21)( 5,11,19)( 6,12,18)( 7, 9,17)(26,27,29)
gap> lub:=(5,9,21)(6,10,24)(8,12,22)(18,2,16)(26,27,30);
( 2,16,18)( 5, 9,21)( 6,10,24)( 8,12,22)(26,27,30)
gap> rdf:=(4,14,20)(1,15,19)(3,13,17)(7,11,23)(25,28,29);
( 1,15,19)( 3,13,17)( 4,14,20)( 7,11,23)(25,28,29)
gap> rdb:=(3,15,23)(2,14,24)(4,16,22)(8,10,20)(25,28,30);
( 2,14,24)( 3,15,23)( 4,16,22)( 8,10,20)(25,28,30)
gap> ldf:=(7,13,19)(6,16,20)(8,14,18)(4,12,24)(26,28,29);
( 4,12,24)( 6,16,20)( 7,13,19)( 8,14,18)(26,28,29)
gap> ldb:=(8,16,24)(5,13,23)(7,15,21)(3,9,19)(26,28,30);
( 3, 9,19)( 5,13,23)( 7,15,21)( 8,16,24)(26,28,30)
gap> G:=Group(ruf,rub,luf,lub,rdf,rdb,ldf,ldb);
Group( ( 1,11,17)( 2,12,20)( 4,10,18)( 6,14,22)(25,27,29), ( 1, 9,23)
( 2,10,22)( 3,11,21)( 5,15,17)(25,27,30), ( 1,13,21)( 5,11,19)( 6,12,18)
( 7, 9,17)(26,27,29), ( 2,16,18)( 5, 9,21)( 6,10,24)( 8,12,22)(26,27,30), 
( 1,15,19)( 3,13,17)( 4,14,20)( 7,11,23)(25,28,29), ( 2,14,24)( 3,15,23)
( 4,16,22)( 8,10,20)(25,28,30), ( 4,12,24)( 6,16,20)( 7,13,19)( 8,14,18)
(26,28,29), ( 3, 9,19)( 5,13,23)( 7,15,21)( 8,16,24)(26,28,30) )
gap> (1,11,17) in G;
false
gap> Size(G);
37791360
gap> (1,11,17)(2,10,22) in G;
false
gap> (1,11,17)(5,9,21) in G;
false
gap> (1,11,17)(5,21,9) in G;
true
gap> (1,11,17)(2,22,10) in G;
false
gap> (1,11,17)(6,12,18) in G;
false
gap> (1,11,17)(6,18,12) in G;
false
gap> quit;