gap> g:=(15,12,21,18,30,27,14,20,6,16,13,26,23,19)(25,24,29,28)(17,22);
( 6,16,13,26,23,19,15,12,21,18,30,27,14,20)(17,22)(24,29,28,25)
gap> g in G;
true
gap> w1:=FactorPermGroupElement(G,w);
Error, Variable: 'w' must have a value
gap> w1:=FactorPermGroupElement(G,g);
g1^-1*g3^-1*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2*g1^-2*g3^3*g1^2*g2^-1*g1^-2*g3*g1^2\
*g2*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2*g1^-2*g3^2*g1^2*g2^-1*g1^-2*g3*\
g1^2*g2*g1^-2*g3^-2*g1^2*g2^-1*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^3*g1^-2\
*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2*g1^-2*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-4*g1^-2*\
g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-2*g1^-2*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2*g1^-2*g\
3^-1*g1^2*g2^-1*g1^-2*g3^3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2*\
g1^-2*g3*g1^2*g2^-1*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^2*g1^-2*g3*g1^2*g2\
^-1*g1^-2*g3^-1*g1^2*g2^4*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3*\
g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2^-1*g1^-2*g3^3*g1^2*g2*g1\
^-2*g3^-1*g1^2*g2^-1*g1^-2*g3*g1^2*g2^2*g1^-2*g3^-1*g1^2*g2^2*g1^-2*g3*g1^2*g2\
^-1*g1^-2*g3^-1*g1^2*g2^-4*g1^-2*g3*g1^2*g2*g1^-2*g3^-3*g1^2*g2^-1*g1^-2*g3^2*\
g1^2*g2^-1*g1^-1
gap> w2:=Shrink(G,w1);
g3^-1*g2^-1*g1^-1*g3^-2*g1*g2*g1^-1*g3^3*g1^2*g2^2*g1^-2*g3^-1*g1^2*g2*g1^-2*g\
3*g1^2*g2^-1*g1^-1*g3^-1*g2^-3*g3*g2*g1*g2*g1^-2*g3^-1*g1^2*g2^-6*g1^-1*g3^-6*\
g2^2*g3*g2*g3^2*g1*g2^-1*g1^-1
gap> w3:=Shrink(G,w2);
g3^-1*g2^-1*g1^-1*g3^-2*g1*g2*g1^-1*g3^3*g1^2*g2^2*g1^-2*g3^-1*g1^2*g2*g1^-2*g\
3*g1^2*g2^-1*g1^-1*g3^-1*g2^-3*g3*g2*g1*g2*g1^-2*g3^-1*g1^2*g2^-6*g1^-1*g3^-6*\
g2^2*g3*g2*g3^2*g1*g2^-1*g1^-1
gap> FactorPermGroupElement(G,r1);
g1
gap> FactorPermGroupElement(G,r2);
g2
gap> FactorPermGroupElement(G,r3);
g3
gap> G_g:=Group(g);
Group( ( 6,16,13,26,23,19,15,12,21,18,30,27,14,20)(17,22)(24,29,28,25) )
gap> Size(G_g);
28
gap> g^28;
()
gap> g^14;
(24,28)(25,29)
gap> g^7;
( 6,12)(13,18)(14,19)(15,20)(16,21)(17,22)(23,27)(24,25,28,29)(26,30)
gap> g^4;
( 6,23,21,14,13,15,30)(12,27,16,19,18,20,26)
gap> quit;

g3^-1*g2^-1*g1^-1*g3^-2*g1*g2*g1^-1*
g3^3*g1^2*g2^2*g1^-2*g3^-1*
g1^2*g2*g1^-2*g3*g1^2*g2^-1*g1^-1*
g3^-1*g2^-3*g3*g2*g1*g2*
g1^-2*g3^-1*g1^2*g2^-6*g1^-1*g3^-6*
g2^2*g3*g2*g3^2*g1*g2^-1*g1^-1


w:=[r3inv,r2inv,r1inv,r3inv,r3inv,r1,r2,r1inv,
r3,r3,r3,r1,r1,r2,r2,r1inv,r1inv,r3inv,
r1,r1,r2,r1inv,r1inv,r3,r1,r1,r2inv,r1inv,
r3inv,r2inv,r2inv,r2inv,r3,r2,r1,r2,
r1inv,r1inv,r3inv,r1,
r1,r2,r2,r2,r2,r2,r2,r1inv,
r3,r3,r3,r3,r3,r3,
r2,r2,r3,r2,r3,r3,r1,r2inv,r1inv];