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Does the FRITZ!Box support oversized packets (jumbo frames)?

No, currently the FRITZ!Box does not support Ethernet packets larger than 1518 bytes (jumbo frames).

For the communication between the devices in the FRITZ!Box home network, all data is grouped into single packets (Ethernet frames). The maximum size of user data that can be transmitted in a single data packet is called the Maximum Transmission Unit (MTU) and is set at 1518 bytes in the Ethernet standard IEEE 802.3. The FRITZ!Box forwards all packets that comply with this standard.