Question

What is the order of each group: (c).$S_4$

Short answer

The order of group $S_4$ is $24$.

Step-by-step solution

Permutation

Let $S$ be a non-empty set. A permutation on $S$ is defined as bijective mapping

$f:S\to S$. If, $S=\left\{a_1,a_2,.......,a_n\right\}$.

Then, the number of bijection from$S$ onto $S$ is $n!$.

Let one of the bijection be $f$ which maps $a_i$ to $f\left(a_i\right)$. This is denoted by the symbol,

$\left(\begin{array}{cccc}{a}_1& a_2& ...& a_n\\ f\left(a_1\right)& f\left(a_2\right)& ...& f\left(a_n\right)\\ & & & \end{array}\right)$

Order of a group

The order of a group $G$ is defined as the number of elements in the group.

Conclusion

Since, $S_4$is a group of permutations of 4 elements.

So, the order of $S_4$is given by$4!=24$