Exercise
Consider the following permutation group of order 6:
With which group is it isomorphic?
S3, the symmetric group on 3 letters.
C6, the cyclic group of order 6.
C2 × C3,
the direct product of a cyclic group of order 2 and a cyclic group of order 3.
True. Actualy, these are the images of the permutation representation
given by conjugation, where the numbers 1, 2, 3, 4, 5, 6 correspond to the following
elements of S3:
| no. | element of S3 | |
| 1 | (1,2) | |
| 2 | (2,3) | |
| 3 | (1,3) | |
| 4 | (1,2,3) | |
| 5 | (1,3,2) | |
| 6 | id |
No, the permutation group is not commutative.
No, the permutation group is not commutative.
By the way, this group is isomorphic to the cyclic group of order 6.