It works. Thank you for your tip. I further verified the relevant logic as follows:
In[5]:= << SpaceGroupIrep`
In[38]:= eles =
generateGroup[{"C3+", "C21p", "\[Sigma]h"}, "E", RotTimes]
Table[seteq[RotTimes[#, i] & /@ eles, eles], {i, eles}]
Map[seteq[#, eles] &, Outer[RotTimes, eles, eles]]
Map[seteq[#, eles] &, Transpose@Outer[RotTimes, eles, eles]]
seteq[#, eles] & /@ Transpose@Outer[RotTimes, eles, eles]
Out[38]= {"C21p", "C22p", "C23p", "C3-", "C3+", "E", "S3-", "S3+", "\
\[Sigma]h", "\[Sigma]v1", "\[Sigma]v2", "\[Sigma]v3"}
Out[39]= {True, True, True, True, True, True, True, True, True, True, \
True, True}
Out[40]= {True, True, True, True, True, True, True, True, True, True, \
True, True}
Out[41]= {True, True, True, True, True, True, True, True, True, True, \
True, True}
Out[42]= {True, True, True, True, True, True, True, True, True, True, \
True, True}