What is the order of $U$? Is $\{1, 7\}$ an orbit from $U$?

Question

Let $G: = S_7$ and $U: = \{(17), (1273)\}$. What is the order of $U$? Is $\{1, 7\}$ an Orbit from $U$?

Attempt:

I know/see $(17)$ has the order $2$ and $(1273)$ the order $4$, but I don't know how to show the order for the subgroup.

Orbit: $1^U = \{1,7\}$ (with $1^{id}= 1, 1^{(1273)}= 2, 1^{(1372)} = 3, 1^{(17)}= 7$), so no orbit?