sidereal day
day *****

This so-called sidereal day measures the rotation of the Earth with respect to the stars.

The period of 1436 minutes is called Earth's "sidereal day."

In contrast, the gas giant Jupiter's sidereal day is only 9 hours and 56 minutes.

A sidereal day (the period of rotation) lasts about 58.7 Earth days.

Due to the orbit of the earth around the sun a sidereal day is 4 minutes (1/366th) less than a solar day.

A mean solar day is, therefore, nearly 4 minutes longer than a sidereal day.

A mean sidereal day is about 23 h 56 m 4.1 s in length.

As you see, your calculation of the length of a sidereal day is right on.

For the planet Earth a sidereal day is approximately 23 hours, 56 minutes, and 4 seconds.

For the Earth this is a sidereal day.