fix doctest

docs/src/Experimental/galois.md

@@ -107,10 +107,10 @@ julia> subfields(F)
  (Function Field over Rational Field with defining polynomial a^3 - 108*t^2 - 108*t - 27, -_a^2)
 
 julia> galois_group(F)
-(Group([ (), (1,5)(2,3)(4,6), (1,3,4)(2,5,6) ]), Galois Context for s^6 + 108*t^2 + 540*t + 675)
+(Group([ (1,3,4)(2,5,6), (1,2)(3,6)(4,5) ]), Galois Context for s^6 + 108*t^2 + 540*t + 675)
 
 julia> G, C, k = galois_group(F, overC = true)
-(Group([ (1,3,4)(2,5,6) ]), Galois Context for s^6 + 108*t^2 + 540*t + 675, Number field over Rational Field with defining polynomial x^2 + 12*x + 24336)
+(Group([ (1,4,3)(2,6,5) ]), Galois Context for s^6 + 108*t^2 + 540*t + 675, Number field over Rational Field with defining polynomial x^2 + 12*x + 24336)
 
 ```
 So, while the splitting field over `Q(t)` has degree `6`, the galois group there

experimental/GaloisGrp/GaloisGrp.jl

@@ -2272,7 +2272,7 @@ julia> galois_quotient(C, 6)
  Number field over Rational Field with defining polynomial x^6 + 324*x^4 - 4*x^3 + 34992*x^2 + 1296*x + 1259716
 
 julia> galois_group(ans[1])
-(Group([ (), (1,5)(2,4)(3,6), (1,2,3)(4,5,6) ]), Galois Context for x^6 + 324*x^4 - 4*x^3 + 34992*x^2 + 1296*x + 1259716 and prime 13)
+(Group([ (1,2,3)(4,5,6), (1,4)(2,6)(3,5) ]), Galois Context for x^6 + 324*x^4 - 4*x^3 + 34992*x^2 + 1296*x + 1259716 and prime 13)
 
 julia> is_isomorphic(ans[1], G)
 true
@@ -2372,7 +2372,7 @@ functions and the coefficients of the polynomial.
 julia> Qx, x = QQ["x"];
 
 julia> i = galois_ideal(galois_group(x^4-2)[2])
-ideal(x4^4 - 2, x3^3 + x3^2*x4 + x3*x4^2 + x4^3, x2^2 + x2*x3 + x2*x4 + x3^2 + x3*x4 + x4^2, x1 + x2 + x3 + x4, -x1*x2 - x1*x3 - x2*x4 - x3*x4)
+ideal(x4^4 - 2, x3^3 + x3^2*x4 + x3*x4^2 + x4^3, x2^2 + x2*x3 + x2*x4 + x3^2 + x3*x4 + x4^2, x1 + x2 + x3 + x4, x1*x4 + x2*x3, x1^2*x4^2 + x2^2*x3^2 - 4, x1^4 - 2, x2^4 - 2, x3^4 - 2, x4^4 - 2)
 
 julia> k, _ = number_field(i);