Is there any code to calculate the subgroup generated by the permutations

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Consider the Symmetric Group $S_4$

I have three permutations namely $(3,4), (1,2), (1,3)(2,4)$ .

How to find the subgroup generated by these permutations ?

Is there any code to calculate in Sagemath the subgroup generated by the permutations given above?

As an example the code should work like this :

If I input $(12)$ the code should give ${(12),e}$

Can someone help please?

1 Answer

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sage: G = SymmetricGroup(4)
sage: H = G.subgroup([(1,2)])
sage: list(H)
[(), (1,2)]

Here () denotes the identity permutation.

Thank you so very much

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