What are the relative permeability and electrical conductivity of $rm GaAs$?

GaAs is not a magnetic material, so you can probably just use μ_r=1, depending just exactly how accurate you need your simulation to be.

As for the conductivity, it will depend on how the material is doped, the temperature, and the frequency of the signals you are interested in.

If you know the doping, you can estimate the conductivity from

$sigma=nemu_c$,

where σ is conductivity, n is carrier density, e is the elementary charge, and $mu_c$ is the carrier mobility. You can get estimates of carrier mobility over temperature from, for example, the Ioffe Institute. Unfortunately, depending on exactly what kind of simulation you are doing, coming up with an accurate value for the mobility can be quite complicated.

Note that n might also depend on temperature, particularly for near-intrinsic material or for very low temperatures.

GaAs permeability is essentially 1. The conductivity, on the other hand, can be quite variable. GaAs is a semiconductor whose electrical properties are easily manipulated through doping.

Your best bet might be to bound the problem from the lowest possible conductivity in GaAs to the moderately high mobility of a doped substrate. Usually resistivity, the reciprocal of conductivity is specified. A Google search of resistivity of semi-insulating GaAs will give you the low ball value for conductivity. This link has lots of values for that case:

The relationship between the resistivity of semi-insulating GaAs and MESFET properties

The numbers range from 1E6 ohm cm to 1E8 ohm cm Which translates to conductivity of 1E-6 to 1E-8 /ohm cm.

In the doped case you can take a heavy doping for GaAs of about 1E18 /$ cm^3 $ and a mobility of about 1000 $ cm^2 / V sec $. This translates to conductivity of about 500 / ohm cm. The plot below shows resistivity, the usually specified parameter.

If you simulate the high and the low case it should give a good idea if conductivity is a critical parameter.

A really good reference for semiconductor electrical properties is:

Properties of Semiconductor Alloys: Group‐IV, III–V and II–VI Semiconductors by Sadao Adachi