Well your phone supports nearly any wireless standard you would come across.
Wi-Fi 802.11 a/b/g/n/ac, dual-band
Your notebook(if i trust google) should support B(11megabit/sec),G(54megabit/sec),N(150megabit/sec[with supported wireless access point]). while G would not make it(collision avoidance), N should be able to handle your network connection.
Keep us posted about how the wired connection works. Also check out the notebook makers website to ensure you have the latest drivers.
The system is not a fast computer either so maybe some other software is bogging it down.