How is your iMac connected to the modem? Ethernet cable?
Try switching on the iMac's wi-fi and see what shows up in the System Preferences/Network dialogue. If you turn on Wi-Fi, you might find your modem in the list of available networks. Or, on the back of the modem, there might be login details?
iMac (19,1, 3.1 GHz i5, 12.7.4, 40 Gb RAM); MacBook Air (1.8 Ghz, 8 Gb RAM, 10.14.6, 256 Gb SSD) Vodafone router and Devolo Wi-Fi Extender, Canon TS8351 printer/scanner.
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