The 6AU5GT is described as a beam pentode and was designed for line output service in low cost television receivers. An alternate design use is as a series pass device in regulated power supplies.
The data-sheet also gives details for use as a Class A amplifier and several single ended designs exist.
A google search suggests that with adjustment of voltages (and with a different pin-out) it could be employed in circuits designed for the 6V6GT where a 5-6 kΩ load is specified.
The rounded end anode has a greater surface area than a 6V6.
The rounded end with central flanges for fixing and maximum heat dissipation.
The wide glass tube envelope is 29 mm in diameter, and excluding the IO base pins is 61 mm tall.
Reference: Data-sheet. Type 6AU5GT was first introduced in 1949. See also1949 adverts.