[Math] Find permutation $B$ given $B^4 =(2143567)$

Question

Let $ B\in S_7 $ and $ B^4 =(2143567)$. Find B.

How to find $B$? All I know is that $B^7 $ is identity permutation because it is a 7 cycle. So $(B^4)^2$ should be B?

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Reference:

Exercise 5.31 from 'Contemporary Abstract Algebra' by Joseph A. Gallian

Answer 1

$B$ is a $7-$ cycle hence $B^7=I\implies B^8=B$

Now from $B^4$ find $B^8$