Examples of Groups of Permutations

Question

Find a four-element abelian subgroup S₅. Write its table.

Answer 1

A simple example could be with this one isomorphic to C₄.

 

Permutations:

 

A: (1)(2)(3)(4)(5) = Id

B: (1 2 3 4)(5)

C: (1 3)(2 4)(5)

D: (1 4 3 2)(5)

 

Table:

× | A  B  C  D

--+------------

A | A  B  C  D

B | B  C  D  A

C | C  D  A  B

D | D  A  B  C