[GAP Forum] Symmetrising presented group from a given presentation

[Minghui Liu]

Dear GAP users,

I have the following question on inputting symmetrised relations in a group.

Let G be a group generated by x_1, x_2, x_3, x_4 with one relation for
example x_1*x_2*x_3^(-1)*x_4^(-2). Now I wish to let the symmetric group
S_4 on 4 letters acts on this relation and therefore obtain a total of
4!=24 relators. For example, one of the obtained relator is
x_2*x_3*x_4^(-1)*x_1^(-2). Is there any easy way for me to write all 24
relators in GAP?

Thank you!

Minghui