What type of 5.5mm DC connector is this
It is a female coaxial power connector.  The notches are just so that the center contact can expand when it plugs onto the male connector.

5.5mm is a standard OD, 2.1mm is a standard pin diameter.  Not all connector manufacturers use the same contact system, so even though the inner contact does not look the same, as long as it is a 5.5mm x 2.1mm connector, it should be compatible.

Note that different contact styles support different current levels, so make sure that if you are looking to replace an existing connector that you get one rated for the expected current requirements.  Or, you could just get the highest current one you can find, if you don't know the current.  Judging from the wires left on the one in the picture, it does not look particularly high current.