We present a Rabi-type measurement of two ground-state hydrogen hyperfine transitions performed in two opposite external magnetic field directions. This puts first constraints at the level of Image 1 on a set of coefficients of the Standard Model Extension, which were not measured by previous experiments. Moreover, we introduce a novel method, applicable to antihydrogen hyperfine spectroscopy in a beam, that determines the zero-field hyperfine transition frequency from the two transitions measured at the same magnetic field. Our value, Image 2, is in agreement with literature at a relative precision of 0.44 ppb. This is the highest precision achieved on hydrogen in a beam, improving over previous results by a factor of 6.