We report the first laser-radio-frequency double resonance spectrum of a simple lanthanide compound, the paramagnetic radical (YbF)-Yb-174. Measurements of the rf intervals as a function of the rotational quantum number N allow us to determine precise spin-rotation and fluorine hyperfine interaction coupling constants for the X (2) Sigma(+) (upsilon = 0 and upsilon = 1) ground states of (YbF)-Yb-174. The results for upsilon = 0 are gamma(0)=-13.424 00(16) MHz, gamma(1)=3.982 3(11) kHz, gamma(2)=-25(1) mHz, b(0)=141.795 6(5) MHz, b(1)=-0.510(11) kHz, c=85.402 6(14) MHz, C=20.38(13) kHz. For upsilon = 1 they are gamma(0)=-33.811 8(7) MHz, gamma(1)=4.323(6) kHz, gamma(2)=-28(9) mHz, b(0)=139.89(4) MHz, b(1)=-0.7(4) kHz, c=86.75(5) MHz, C=18.3(1) kHz. A direct microwave measurement of the first rotational interval in X (2) Sigma(+) (upsilon = 0) gives the rotational constant B-0=0.241 292 7(7) cm(-1). Finally, the Stark shift of hyperfine transitions in the first two rotational states of X (2) Sigma(+) (upsilon = 0) an analyzed to determine the electric dipole moment mu(e) = 3.91(4) D. We find that although the gross structure of YbF in its ground state resembles that of an alkaline earth monofluoride, the 4f shell is evidently important even in the low-lying excited states and leads to unusual behavior in the ground-state magnetic structure.