Is the mobile company a central enterprise or a state-owned enterprise?

It is a state-owned enterprise and a central enterprise.

The ultimate controller of China Mobile: China Mobile Communications Group Co., Ltd. (holding 69.82% shares of China Mobile Communications Group Co., Ltd.) is controlled by China Mobile Communications Group Co., Ltd., while China Mobile Communications Group Co., Ltd. is actually controlled by the State Council 100%, indicating that China Mobile is a central enterprise. Central enterprises belong to state-owned enterprises, which include central enterprises. In China, important livelihood industries such as communication, energy, banking, transportation and grain are controlled by state-owned enterprises.