All Gatwick Express trains are operated by Southern, as Gatwick Express is not a TOC, it's now a brand name. This particular service may be in Gatwick Express livery but that doesn't mean it's operating a Gatwick Express service. Trains at East Croydon often turn up in a different livery to what you might expect!
There are regular diagrams for the 442s but I can't remember what they are, but there aren't many of them. If the 0833 is convenient for you, then aim to get that each day!