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This can be done using interface to GAP:

G=SymmetricGroup(3); a=G((1,2)); b=G((2,3))
x = G( gap(f'RepresentativeAction({gap(G)},{b},{a})') )
print( x*a == b*x )

This can be done using interface to GAP:

G=SymmetricGroup(3); a=G((1,2)); b=G((2,3))
x = G( gap(f'RepresentativeAction({gap(G)},{b},{a})') )
gap.RepresentativeAction(G,b,a)
print( x*a == b*x )

This can be done using interface to GAP:

G=SymmetricGroup(3); a=G((1,2)); b=G((2,3))
x = gap.RepresentativeAction(G,b,a)
G( gap.RepresentativeAction(G,b,a) )
print( x*a == b*x )