  We use multifractal finite-size scaling to perform a high-precision numerical
study of the critical properties of the Anderson localization-delocalization
transition in the unitary symmetry class, considering the Anderson model
including a random magnetic flux. We demonstrate the scale invariance of the
distribution of wavefunction intensities at the critical point and study its
behavior across the transition. Our analysis, involving more than $4\times10^6$
independently generated wavefunctions of system sizes up to $L^3=150^3$, yields
accurate estimates for the critical exponent of the localization length,
$\nu=1.446 (1.440,1.452)$, the critical value of the disorder strength and the
multifractal exponents.
