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typeset_mode(True, display=False)

S3=SymmetricGroup(3); S3
⟨(1,2,3),(1,2)⟩\langle (1,2,3), (1,2) \rangle
︠f6f5c642-d0c8-4d06-9a2a-6c4ecfafa2d3︠
SymmetricGroup.3.list()
[$$, $(1,3,2)$, $(1,2,3)$, $(2,3)$, $(1,3)$, $(1,2)$]
a = S3((1,2));a
(1,2)(1,2)
b= S3((2,3));b
(2,3)(2,3)
a*b
(1,3,2)(1,3,2)
b*a
(1,2,3)(1,2,3)
class NewSymmetricGroupElement(sage.groups.perm_gps.permgroup_element.SymmetricGroupElement):
    def __mul__(self, other):
        """Calling the original class method with order inverted"""
        print(self, other)
        return sage.groups.perm_gps.permgroup_element.SymmetricGroupElement._mul_(other, self)
    
class NewSymmetricGroup(SymmetricGroup):
    def _element_class(self):
        return NewSymmetricGroupElement

NS3=NewSymmetricGroup(3); NS3
⟨(1,2,3),(1,2)⟩\langle (1,2,3), (1,2) \rangle
c=NS3((1,2)); type(c)
d=NS3((2,3)); type(d)
<type 'sage.groups.perm_gps.permgroup_element.SymmetricGroupElement'> <type 'sage.groups.perm_gps.permgroup_element.SymmetricGroupElement'> 
︠690ea8fc-cb69-47d5-9340-3c2876acddaas︠
c*d # produces (1,3,2) but I would have expected (1,2,3), i.e. b*a above
(1,3,2)(1,3,2)
d*c # produces (1,2,3) but I would have expected (1,3,2), i.e. a*b above
(1,2,3)(1,2,3)