Specifically, a radiation-hardened 486. The type of equipment that can survive in space lags significantly behind what you would consider modern on a desktop computer. For example, the radiation-hardened PowerPC G3 is a popular choice. It will power the 2020 Mars rover too: https://en.m.wikipedia.org/wiki/RAD750
Yep, the original main computer was a 1.25 MHz (!) DF-224 [1]. It was augmented on Servicing Mission 1 in 1993 with a 15 Mhz 80386 co-processor [2]. The 80486 was installed in 1999 on Servicing Mission 3A (STS-103) [2].
