P = PolynomialRing(QQ, 'x', 6)
xs = x0,x1,x2,x3,x4,x5 = P.gens()

def act_single(g, p):
  return p.subs({xs[i-1]: xs[j-1] for i, j in g.dict().items()})

def act_all(G, p):
  return [act_single(g, p) for g in G]

G = PermutationGroup([[(2,4,6,5,3)], [(1,2),(3,5),(4,6)]])
p = x0^2 + x0*x1
print(G[:10])
print(act_all(G, p)[:10])