verifying the sizes of a group acting on a set

Question

Is $S_4$ a group of size four and $X={1,2,3,4}$ a set of size four? Need clarification on this.

just wan to be clear on the sizes of the group and the set.

Answer 1

The order of $S_4$ is $4!$ ("order" is the terminology used for "cardinality" when referring to groups). The size (or, I prefer, cardinality) of $X$ is $4$.

Does that help?