We report the creation of a sample of over 1000 ultracold $^{87}$RbCs molecules in the lowest rovibrational ground state, from an atomic mixture of $^{87}$Rb and Cs, by magnetoassociation on an interspecies Feshbach resonance followed by stimulated Raman adiabatic passage (STIRAP). We measure the binding energy of the RbCs molecule to be $h c times 3811.576(1)$ cm$^{-1}$ and the $|v=0, J=0>$ to $|v=0, J=2>$ splitting to be $h times 2940.09(6)$ MHz. Stark spectroscopy of the rovibrational ground state yields an electric dipole moment of 1.225(3)(8) D, where the values in parentheses are the statistical and systematic uncertainties, respectively. We demonstrate that a space-fixed dipole moment of 0.355(2)(4) D is accessible in RbCs, which is substantially higher than in previous work.