Unassigned — it sits in the long empty 7748-7776 gap below the game-server crowd on 7777.
IANA's last registration before this gap is 7747 (prgp, Put/Run/Get Protocol); 7748 through 7776 are unassigned, 7749 among them. Nmap has no service name for it and scores it near 0.015% open frequency. Nothing standard claims it, so treat any listener as application-specific and identify it locally.
Expose with care
Unregistered port, unknown service — resolve the owning process before making a firewall decision.
$ sudo lsof -nP -iTCP:7749 -sTCP:LISTENSeen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.