We have measured upper-critical-field $H_{text c2}$, specific heat C, and tunneling spectra of the intermetallic perovskite superconductor MgCNi${}_3$ with a superconducting transition temperature $T_{text c}approx 7.6$ K. Based on these measurements and relevant theoretical relations, we have evaluated various superconducting parameters for this material, including the thermodynamic critical field $H_{text c}$(0), coherence length $xi$(0), penetration depth $lambda$(0), lower-critical-field $H_{text c1}$(0), and Ginsberg-Landau parameter $kappa$(0). From the specific heat, we obtain the Debye temperature $it Theta_{text D} approx$ 280 K. We find a jump of $Delta C/gamma T_{text c}$=2.3 at $T_{text c}$ (where $it gamma$ is the normal state electronic specific coefficient), which is much larger than the weak coupling BCS value of 1.43. Our tunneling measurements revealed a gap feature in the tunneling spectra at $it Delta$ with $2it {Delta}/{text k}_{text B}T_{text c}approx$ 4.6, again larger than the weak-coupling value of 3.53. Both findings indicate that MgCNi$_3$ is a strong-coupling superconductor. In addition, we observed a pronounced zero-bias conductance peak (ZBCP) in the tunneling spectra. We discuss the possible physical origins of the observed ZBCP, especially in the context of the pairing symmetry of the material.
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