gap> Read("c:/gap/group.g");
gap> G;
Group( (1,2,3), ( 4, 7,10)( 5, 8,11)( 6, 9,12), (13,18,23)(14,19,24)(15,20,25)
(16,21,26)(17,22,27)(28,32,36)(29,31,34)(30,35,33), (17,32,18), ( 6,30,20)
( 7,15,35)(16,31,19), ( 1,28,22)( 2,13,36)( 3,27,23)( 4,33, 9)( 5,29,21)
( 8,14,34)(10,12,25)(11,26,24), (13,27,28), ( 4,25,30)(12,33,15)(14,26,29), 
( 1,23,32)( 2,22,18)( 3,36,17)( 5,24,31)( 6,10,35)( 7, 9,20)( 8,21,19)
(11,34,16), (22,36,23), ( 9,35,25)(10,20,33)(21,34,24), ( 1,17,13)( 2,32,27)
( 3,18,28)( 4, 6,15)( 5,16,14)( 7,30,12)( 8,31,26)(11,19,29) )
gap> Size(G);
906992640
gap> N:=Size(G);
906992640
gap> N/12;
75582720
gap> edgeflip2:=(6,7)(12,4);
( 4,12)( 6, 7)
gap> edgeswap:=(6,7)(12,4);
( 4,12)( 6, 7)
gap> edgeswap in G;
true
gap> Read("c:/gap/gap3r4p3/lib/abstab.g");
The record 'descriptions' contains brief descriptions of the functions
in this file.
Functions of importance: MakeAbStabChain, FactorPermGroupElement, Shrink
gap> FactorPermGroupElement(G,edgeswap);
g2*g11*g2^-2*g11^-1*g2^2*g11^-1*g2^-2*g11^-1*g2^2*g11*g2^-1*g3*g2*g11^-1*g2^-1\
*g3^-1*g2^-1*g11*g2*g3*g2*g11*g2^-1*g3^-1*g2*g11*g2^-2*g11^-1*g2
gap> FactorPermGroupElement(G,u1);
g1
gap> FactorPermGroupElement(G,u2);
g2
gap> FactorPermGroupElement(G,u3);
g3
gap> FactorPermGroupElement(G,r1);
g3*g10*g3^-1
gap> FactorPermGroupElement(G,r2);
g3*g2*g11*g2^-1*g3^-1
gap> FactorPermGroupElement(G,r3);
g6
gap> FactorPermGroupElement(G,l1);
g3^-1*g10*g3
gap> FactorPermGroupElement(G,l2);
g2*g11*g2^-2*g11^-1*g2^2*g11^-1*g2^-2*g11^-1*g2^2*g11*g2^-1*g3*g2*g11^-1*g2^-1\
*g3^-1*g2^-1*g11*g2*g3*g2*g11*g2^-1*g3^-1*g2*g11*g2^-2*g11^-1*g2^2*g11^-1*g2^-\
2*g11^-1*g2*g3*g2*g11*g2^-1*g3^-1*g2*g11*g2^-1*g3*g2*g11^-1*g2^-1*g3^-1*g2*g11\
^-1*g2^-2*g11^-1*g2*g3^-1*g2*g11*g2^-1*g3
gap> FactorPermGroupElement(G,l3);
g9
gap> FactorPermGroupElement(G,b1);
g10
gap> FactorPermGroupElement(G,b2);
g11
gap> FactorPermGroupElement(G,b3);
g12
gap> FactorPermGroupElement(G,edgeswap);
g2*g11*g2^-2*g11^-1*g2^2*g11^-1*g2^-2*g11^-1*g2^2*g11*g2^-1*g3*g2*g11^-1*g2^-1\
*g3^-1*g2^-1*g11*g2*g3*g2*g11*g2^-1*g3^-1*g2*g11*g2^-2*g11^-1*g2
gap> Shrink(G,edgeswap);
g6^-1*g2*g11*g3*g11*g2^-1*g11^-1*g3^-1*g11^-1*g6
gap> g:=Shrink(G,edgeswap);
g6^-1*g2*g11*g3*g11*g2^-1*g11^-1*g3^-1*g11^-1*g6
gap> gg:=Shrink(G,g);
g6^-1*g2*g11*g3*g11*g2^-1*g11^-1*g3^-1*g11^-1*g6
gap> (6,7) in G;
false
gap> quit;

edgeswap:=r3^(-1)*u2*b2*u3*b2*u2^(-1)*b2^(-1)*u3^(-1)*b2^(-1)*r3;