Alternating Group on 4 Letters

Group Example
Let $S_4$ denote the symmetric group on $4$ letters.

The alternating group on $4$ letters $A_4$ is the kernel of the mapping $\sgn: S_4 \to C_2$.

Cycle Notation
It can be expressed in the form of permutations given in cycle notation as follows:

Cayley Table
The Cayley table of $A_4$ can be written: