Group Theory - Exercise - Continued

I have been working on the problem that I published last week....

S3
Element - Order - Permutation Sign - Transpositions
() - 1 - +1 - ()
(1,2,3) - 3 - +1 - (1,2)(1,3)
(1,3,2) - 3 - +1 - (1,3)(1,2)
(1,2) - 2 - -1 - (1,2)
(1.3) - 2 - -1 - (1,3)
(2,3) - 2 - -1 - (1,2)

Now take the following subgroup of A5:
() - 1 - +1 - ()
(3,4,5) - 3 - +1 - (3,4)(4,5)
(3,5,4) - 3 - +1 - (3,5)(3,4)
(1,2)(4,5) - 2 -  +1 - (1,2)(4,5)
(1,2)(3,4) - 2 -  +1 - (1,2)(3,4)
(1,2)(3,5) - 2 -  +1 - (1,2)(3,5)
This is a group with S3 structure but conisting entirely of even permutations.

If any group of n elements is a subgroup of A(n+2) it must have an isomorphic copy consisting of all positive permutations.