\Sym(\perm{123}{123}) & 4 & 1, 4, 32, 368, 4952, 68256, \ensuremath{\cdots} & {\rm new} \\
\hline
\Sym(\perm{123}{132}) & 24 & 1, 4, 12, 4, 4, 4, \ensuremath{\cdots} & {\rm new} \\
\hline
\Sym(\perm{132}{213}) & 8 & 1, 4, 28, 256, 2704, 31192, \ensuremath{\cdots} & {\rm new} \\
\hline
