It looks like a an SO239, but the center portion does not have the standard white insulating material. It's just insulated by open air space.
While an N connector will not have the insulating material around the center conductor, most SO239 connectors do...but there is a variant SO-239 that has minimal material, just enough to keep the center conductor socket centered. Most of the dielectric material between the inner and outer conductor is air.
As near as I can tell, this is done to try to make the impedance of the UHF connector closer to 50 ohms. UHF connectors are known to be non-constant impedance connectors (unlike BNC or Type N connectors). The ratio of outer conductor and inner conductor diameters changes across the length of the connector, meaning the characteristic impedance of the connector changes. This is not a big deal on HF, but becomes more of a concern at VHF and above.
I have never seen these connectors for sale anywhere, but have seen them on SWR/power meters, and on VHF and above radios/antennas.
It sounds like your antenna has this variant of a SO239. This would make sense to use with a discone.
Redhat is right - this thread would be a lot shorter if we had included pictures.