Table 1 \(C_{3v}\) permutations
From: Automatic procedure for generating symmetry adapted wavefunctions
\({\hat{E}}\) | \(({\hat{E}})\quad ({\hat{C}}_3)\quad ({\hat{C}}_3^2)\quad ({\hat{\sigma }})\quad ({\hat{\sigma }}')\quad ({\hat{\sigma }}'')\) |
\({\hat{C}}_3\) | \(({\hat{E}}\;{\hat{C}}_3\;{\hat{C}}_3^2)\quad ({\hat{\sigma }}\;{\hat{\sigma }}'\;{\hat{\sigma }}'')\) |
\({\hat{C}}_3^2\) | \(({\hat{E}}\;{\hat{C}}_3^2\;{\hat{C}}_3)\quad ({\hat{\sigma }}\;{\hat{\sigma }}''\;{\hat{\sigma }}')\) |
\({\hat{\sigma }}\) | \(({\hat{E}}\;{\hat{\sigma }})\quad ({\hat{C}}_3\;{\hat{\sigma }}'')\quad ({\hat{C}}_3^2\;{\hat{\sigma }}')\) |
\({\hat{\sigma }}'\) | \(({\hat{E}}\;{\hat{\sigma }}^{'})\quad ({\hat{C}}_3\;{\hat{\sigma }})\quad ({\hat{C}}_3^2\;{\hat{\sigma }}'')\) |
\({\hat{\sigma }}''\) | \(({\hat{E}}\;{\hat{\sigma }}'')\quad ({\hat{C}}_3\;{\hat{\sigma }}')\quad ({\hat{C}}_3^2\;{\hat{\sigma }})\) |