Solar active regions (ARs) are the major sources of two kinds of the most violent solar eruptions, namely flares and coronal mass ejections (CMEs). The largest AR in the past 24 years, NOAA AR 12192, crossed the visible disk from 2014 October 17 to 30, unusually produced more than one hundred flares, including 32 M-class and 6 X-class ones, but only one small CME. Flares and CMEs are believed to be two phenomena in the same eruptive process. Why is such a flare-rich AR so CME-poor? We compared this AR with other four ARs; two were productive in both and two were inert. The investigation of the photospheric parameters based on the SDO/HMI vector magnetogram reveals that the flare-rich AR 12192, as the other two productive ARs, has larger magnetic flux, current and free magnetic energy than the two inert ARs, but contrast to the two productive ARs, it has no strong, concentrated current helicity along both sides of the flaring neutral line, indicating the absence of a mature magnetic structure consisting of highly sheared or twisted field lines. Furthermore, the decay index above the AR 12192 is relatively low, showing strong constraint. These results suggest that productive ARs are always large and have enough current and free energy to power flares, but whether or not a flare is accompanied by a CME is seemingly related to (1) if there is mature sheared or twisted core field serving as the seed of the CME, (2) if the constraint of the overlying arcades is weak enough.