  A canonical variable coefficient nonlinear Schr\"{o}dinger equation with a
four dimensional symmetry group containing $\SL(2,\mathbb{R})$ group as a
subgroup is considered. This typical invariance is then used to transform by a
symmetry transformation a known solution that can be derived by truncating its
Painlev\'e expansion and study blow-ups of these solutions in the $L_p$-norm
for $p>2$, $L_\infty$-norm and in the sense of distributions.
