Ref: NEC Table 310.16
8 AWG is rated for 50 Amps if it is not NM or other 60 C wire.
You need 6 AWG in THWN for outside. You can usually use 8 AWG for the neutral and 10 AWG for the ground unless your inspector gets picky. My last one didn't bother with code and wanted 8 for the ground.
It will all fit in a 3/4 conduit.