Creating a Finite Group in Sage

Question

Create a finite group in $S_4$ in sage

$H=\{(),(1,2)(3,4),(1,3)(2,4),(1,4)(2,3) \}$

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can make a cyclic group out of them with

S4 = SymmetricGroup(4)

v1=S4((id))

v2 = S4("(1,2)(3,4)")

v3 = S4("(1,3)(2,4)")

v4=S4("(1,4)(2,3)")

v2*v3

can go one to find right or left cosets

S4.cosets(H, side='right')

S4.cosets(H, side='left')

H.list() will list

make table

H.cayley_table()

can find sing of elements of $S_4$

sigma.sign()

but cant make that group

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after commnets

Link sage example its "not psude code"!!

https://cocalc.com/projects/63d635fd-6ae0-4732-afdb-6ef4f5103c5d/files/2017-10-18-083014.sagews

Answer 1

Build your subgroup with the following code:

S4=SymmetricGroup(4); H=S4.subgroup([S4("(1,2)(3,4)"),S4("(1,3)(2,4)"),S4("(1,4)(2,3)")])

The reason your code doesn't work is that you only defined a subset of $S_4,$ and sage got grumpy because it believes that objects have an associated "type."