So the adapter, there are several ways to get there. This is one of the many. Click on the Start button, than right click Computer and choose Properties, in the upper left corner you will find Device Control, open it.
In the Device Control Panel you will find an entry Network Adapters, click on it, than you will see a WiFi adapter, right click on it and go for the Properties.
In the Properties Panel of the WiFi adapter you click on the advanced tab, there are the parameters you want to see. B.t.w. they differ from adapter to adapter.
Of special interest are:
802.11n modus
standard wireless ad-hoc modus
wireless modus
I can't say what the settings are in your location, make them the same as on the other laptop.
And a last point, most...