  Aims. We aim to systematically study the properties of the different
transitions of the dense molecular gas tracer HC3N in galaxies. Methods. We
have conducted single-dish observations of HC3N emission lines towards a sample
of nearby gas-rich galaxies. HC3N(J=2-1) was observed in 20 galaxies with
Effelsberg 100-m telescope. HC3N(J=24-23) was observed in nine galaxies with
the 10-m Submillimeter Telescope (SMT). Results. HC3 N 2-1 is detected in three
galaxies: IC 342, M 66 and NGC 660 (> 3 {\sigma}). HC3 N 24-23 is detected in
three galaxies: IC 342, NGC 1068 and IC 694. This is the first measurements of
HC3N 2-1 in a relatively large sample of external galaxies, although the
detection rate is low. For the HC3 N 2-1 non-detections, upper limits (2
{\sigma}) are derived for each galaxy, and stacking the non-detections is
attempted to recover the weak signal of HC3N. But the stacked spectrum does not
show any significant signs of HC3N 2-1 emission. The results are also compared
with other transitions of HC3N observed in galaxies. Conclusions. The low
detection rate of both transitions suggests low abundance of HC3N in galaxies,
which is consistent with other observational studies. The comparison between
HC3N and HCN or HCO+shows a large diversity in the ratios between HC3N and HCN
or HCO+. More observations are needed to interpret the behavior of HC3N in
different types of galaxies.
