The cable is plugged on a Zyxel VES1724-56 DSLAM. It is a VDSL cable.
I can't find a good authoritative source, but as per your picture, we also use in our ADSL and VDSL DSLAMs/MSANs.
It is an RJ21 connector, sometimes also called an RJ21X connector.
This page has the more accurate picture I can find. That is how we often use them, pack to a patch panel to break out into RJ11 ports (for testing in the LAB) or back to krone blocks in a live PoP.
This page has a wiring guide.
This is variously called an Amphenol, a Telco 50-way connector, and sometimes (rarely) a Centronics. In the kinds of places where you find DSLAMs like this unit -- communication service providers-- the term "Amphenol" is what I've heard most. Basically it is a very convenient form factor for aggregating connections. In this case, the DSLAM is going to be aggregating multiple connections from end user premises (houses, apartments etc) and so instead of plugging in dozens of individual lines they are aggregated into the Amphenol and connected.
Amphenol was the standard connector used in telcos for aggregating DS1s. At higher densities other connectors are used, such as coax for DS3. These days fiber is also used a lot, for even higher densities.