  The disorder induced metal--insulator transition is investigated in a
three-dimensional simple cubic lattice and compared for the presence and
absence of time-reversal and spin-rotational symmetry, i.e. in the three
conventional symmetry classes. Large scale numerical simulations have been
performed on systems with linear sizes up to $L=100$ in order to obtain
eigenstates at the band center, $E=0$. The multifractal dimensions, exponents
$D_q$ and $\alpha_q$, have been determined in the range of $-1\leq q\leq 2$.
The finite-size scaling of the generalized multifractal exponents provide the
critical exponents for the different symmetry classes in accordance with values
known from the literature based on high precision transfer matrix techniques.
The multifractal exponents of the different symmetry classes provide further
characterization of the Anderson transition, which was missing from the
literature so far.
