  Comet 73P/Schwassmann-Wachmann 3 has been observed to fragment on several
occasions, yet the cause of its fragmentation remains poorly understood. We use
previously unpublished archival Hubble Space Telescope data taken in 2006 to
study the properties of the primary fragment, 73P-C, in order to constrain the
potential fragmentation mechanisms. Currently the literature presents a wide
range of measured rotational periods, some of which suggest that the nucleus
might have split due to rotational instability. However, we find the most
likely value of the rotation period to be 10.38 $\pm$ 0.04 hours (20.76 $\pm$
0.08 hours if double-peaked), much longer than the critical period for
rotational instability for any reasonable nucleus density and shape, even in
the absence of tensile strength. We also find strong, cyclic photometric
variations of about 0.31 $\pm$ 0.01 magnitudes in the central light from this
object, while similar variations with a smaller range are apparent in the
surrounding dust coma. These observations are compatible with rotational
modulation of the mass loss rate and with dust having a mean outflow speed of
$107 \pm 9$ m s$^{-1}$. Finally, we also estimate the radius of the nucleus to
be 0.4 $\pm$ 0.1 km accounting for dust contamination and assuming a geometric
albedo of 0.04.
