amontero90's profile - activity

From sage documentation I can construct a group as follows:

sage: m1 = matrix(GF(11), [[1,2],[3,4]])
sage: m2 = matrix(GF(11), [[1,3],[10,0]])
sage: G = MatrixGroup(m1, m2);  G
Matrix group over Finite Field of size 11 with 2 generators (
[1 2]  [ 1  3]
[3 4], [10  0]
)

Now I use the following code:

sage: G_p=G.as_permutation_group(); G_p
Permutation Group with generators [(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14,16)(17,18), (1,3,5,7,9,11,2,4,6,8,10)(12,14,13,16,15)(17,18)]

In this case it is true that the generators of G are in correspondence with the generators of G_p. Is this always the case? I mean, if I compute a very complicated group G with lots of generators and its corresponding permutation group G_p, then is it true that G.gens()[i] corresponds to G_p.gens[i]?