| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccc} \text{} & \text{EAZ} & \{1\} & \left\{6_{001},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{3_{001}\right\} & \left\{2_{001},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{3^-{}_{001}\right\} & \left\{6^-{}_{001},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{A}_1 & \text{AI} & 1 & -\sqrt[6]{-1} & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\mathrm{i} & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -(-1)^{5/6} \\ \text{A}_2 & \text{AI} & 1 & (-1)^{5/6} & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) &\mathrm{i}& -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \sqrt[6]{-1} \\ \text{A}_3 & \text{AI} & 1 & -\mathrm{i} & -1 &\mathrm{i}& 1 & -\mathrm{i} \\ \text{A}_4 & \text{AI} & 1 &\mathrm{i}& -1 & -\mathrm{i} & 1 &\mathrm{i}\\ \text{A}_5 & \text{AI} & 1 & -(-1)^{5/6} & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\mathrm{i} & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & -\sqrt[6]{-1} \\ \text{A}_6 & \text{AI} & 1 & \sqrt[6]{-1} & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) &\mathrm{i}& \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & (-1)^{5/6} \\ \end{array} \right)\) |
| B | \(\left(0,\frac{1}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{B}_1 & \text{AI} & 1 & -\mathrm{i} \\ \text{B}_2 & \text{AI} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| C | \(\left(\frac{1}{3},\frac{1}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{001}\right\} & \left\{3^-{}_{001}\right\} \\ \text{C}_1 & \text{CI} & 1 & -1 & 1 \\ \text{C}_2 & \text{AI} & 1 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{C}_3 & \text{AI} & 1 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \end{array} \right)\) |
| D | \(\left(0,0,\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccc} \text{} & \text{EAZ} & \{1\} & \left\{6_{001},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{3_{001}\right\} & \left\{2_{001},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{3^-{}_{001}\right\} & \left\{6^-{}_{001},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{D}_1 & \text{A} & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{D}_2 & \text{A} & 1 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) \\ \text{D}_3 & \text{D} & 1 & -1 & -1 & 1 & 1 & -1 \\ \text{D}_4 & \text{D} & 1 & 1 & -1 & -1 & 1 & 1 \\ \text{D}_5 & \text{A} & 1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -1 & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \text{D}_6 & \text{A} & 1 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & 1 & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) \\ \end{array} \right)\) |
| E | \(\left(0,\frac{1}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,0,\frac{1}{2}\right\}\right\} \\ \text{E}_1 & \text{D} & 1 & -1 \\ \text{E}_2 & \text{D} & 1 & 1 \\ \end{array} \right)\) |
| F | \(\left(\frac{1}{3},\frac{1}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{001}\right\} & \left\{3^-{}_{001}\right\} \\ \text{F}_1 & \text{DIII} & 1 & -1 & 1 \\ \text{F}_2 & \text{AII} & 1 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ \text{F}_3 & \text{AII} & 1 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(\frac{t}{3},\frac{t}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ a_1 & \text{CI} & 1 \\ \end{array} \right)\) |
| \(b\) | \(\left(0,\frac{t}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ b_1 & \text{CI} & 1 \\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{3},\frac{1}{\sqrt{3}},0\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ c_1 & \text{CI} & 1 \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{t}{3},\frac{t}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ d_1 & \text{DIII} & 1 \\ \end{array} \right)\) |
| \(e\) | \(\left(0,\frac{t}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ e_1 & \text{BDI} & 1 \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{t}{3},\frac{1}{\sqrt{3}},\frac{1}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ f_1 & \text{DIII} & 1 \\ \end{array} \right)\) |
| \(g\) | \(\left(0,0,\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccccc} \text{} & \text{EAZ} & \{1\} & \left\{6_{001},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{3_{001}\right\} & \left\{2_{001},\left\{0,0,\frac{1}{2}\right\}\right\} & \left\{3^-{}_{001}\right\} & \left\{6^-{}_{001},\left\{0,0,\frac{1}{2}\right\}\right\} \\ g_1 & \text{A} & 1 & -\sqrt[6]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & -(-1)^{5/6} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_2 & \text{A} & 1 & (-1)^{5/6} e^{-\frac{1}{2}\mathrm{i}\pi t} & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & \sqrt[6]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_3 & \text{A} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & -1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_4 & \text{A} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & -1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_5 & \text{A} & 1 & -(-1)^{5/6} e^{-\frac{1}{2}\mathrm{i}\pi t} & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) & -\sqrt[6]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ g_6 & \text{A} & 1 & \sqrt[6]{-1} e^{-\frac{1}{2}\mathrm{i}\pi t} & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) & (-1)^{5/6} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\) |
| \(h\) | \(\left(0,\frac{1}{\sqrt{3}},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001},\left\{0,0,\frac{1}{2}\right\}\right\} \\ h_1 & \text{A} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ h_2 & \text{A} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\) |
| \(i\) | \(\left(\frac{1}{3},\frac{1}{\sqrt{3}},\frac{t}{2}\right)\) | \(\left( \begin{array}{ccccc} \text{} & \text{EAZ} & \{1\} & \left\{3_{001}\right\} & \left\{3^-{}_{001}\right\} \\ i_1 & \text{AIII} & 1 & -1 & 1 \\ i_2 & \text{A} & 1 & \frac{1}{2} \left(1-\mathrm{i} \sqrt{3}\right) & -\frac{1}{2}\mathrm{i}\left(\sqrt{3}-\mathrm{i}\right) \\ i_3 & \text{A} & 1 & \frac{1}{2} \left(1+\mathrm{i} \sqrt{3}\right) & \frac{1}{2}\mathrm{i}\left(\sqrt{3}+\mathrm{i}\right) \\ \end{array} \right)\) |