Finite Group DatabasebetaFinite Group DatabasebetaOrder 144.
| C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | C19 | C20 | C21 | C22 | C23 | C24 | C25 | C26 | C27 | C28 | C29 | C30 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 2 | 2 | 2 | 2 | 9 | 1 | 2 | 2 | 2 | 2 | 9 | 2 | 4 | 4 | 4 | 4 | 18 | 2 | 4 | 4 | 4 | 4 | 18 | 2 | 4 | 4 | 4 | 4 | 18 |
| order | 1 | 3 | 9 | 9 | 9 | 2 | 2 | 6 | 18 | 18 | 18 | 2 | 4 | 12 | 36 | 36 | 36 | 4 | 4 | 12 | 36 | 36 | 36 | 4 | 4 | 12 | 36 | 36 | 36 | 4 |
| χ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| χ2 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 |
| χ3 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 |
| χ4 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 |
| χ5 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 |
| χ6 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 |
| χ7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
| χ8 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 |
| χ9 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | -2 | -2 | 1 | 1 | 1 | 0 | -2 | -2 | 1 | 1 | 1 | 0 |
| χ10 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | -2 | 1 | −ζ−ζ8 | −ζ2−ζ7 | −ζ4−ζ5 | 0 | -2 | 1 | −ζ−ζ8 | −ζ2−ζ7 | −ζ4−ζ5 | 0 |
| χ11 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | -2 | 1 | −ζ2−ζ7 | −ζ4−ζ5 | −ζ−ζ8 | 0 | -2 | 1 | −ζ2−ζ7 | −ζ4−ζ5 | −ζ−ζ8 | 0 |
| χ12 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | -2 | 1 | −ζ4−ζ5 | −ζ−ζ8 | −ζ2−ζ7 | 0 | -2 | 1 | −ζ4−ζ5 | −ζ−ζ8 | −ζ2−ζ7 | 0 |
| χ13 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 |
| χ14 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 |
| χ15 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | -2 | -2 | 1 | 1 | 1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | -2 | -2 | 1 | 1 | 1 | 0 |
| χ16 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | -2 | 1 | −ζ−ζ8 | −ζ2−ζ7 | −ζ4−ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | -2 | 1 | −ζ−ζ8 | −ζ2−ζ7 | −ζ4−ζ5 | 0 |
| χ17 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | -2 | 1 | −ζ2−ζ7 | −ζ4−ζ5 | −ζ−ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | -2 | 1 | −ζ2−ζ7 | −ζ4−ζ5 | −ζ−ζ8 | 0 |
| χ18 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | -2 | 1 | −ζ4−ζ5 | −ζ−ζ8 | −ζ2−ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | -2 | 1 | −ζ4−ζ5 | −ζ−ζ8 | −ζ2−ζ7 | 0 |
| χ19 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 |
| χ20 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 |
| χ21 | 2 | 2 | -1 | -1 | -1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | -2 | -2 | 1 | 1 | 1 | 0 | -2 | -2 | 1 | 1 | 1 | 0 | 2 | 2 | -1 | -1 | -1 | 0 |
| χ22 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 | -2 | 1 | −ζ−ζ8 | −ζ2−ζ7 | −ζ4−ζ5 | 0 | -2 | 1 | −ζ−ζ8 | −ζ2−ζ7 | −ζ4−ζ5 | 0 | 2 | -1 | ζ+ζ8 | ζ2+ζ7 | ζ4+ζ5 | 0 |
| χ23 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 | -2 | 1 | −ζ2−ζ7 | −ζ4−ζ5 | −ζ−ζ8 | 0 | -2 | 1 | −ζ2−ζ7 | −ζ4−ζ5 | −ζ−ζ8 | 0 | 2 | -1 | ζ2+ζ7 | ζ4+ζ5 | ζ+ζ8 | 0 |
| χ24 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 | -2 | 1 | −ζ4−ζ5 | −ζ−ζ8 | −ζ2−ζ7 | 0 | -2 | 1 | −ζ4−ζ5 | −ζ−ζ8 | −ζ2−ζ7 | 0 | 2 | -1 | ζ4+ζ5 | ζ+ζ8 | ζ2+ζ7 | 0 |
| χ25 | 2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ26 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ27 | 4 | 4 | -2 | -2 | -2 | 0 | -4 | -4 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ28 | 4 | -2 | 2ζ+2ζ8 | 2ζ2+2ζ7 | 2ζ4+2ζ5 | 0 | -4 | 2 | −2ζ−2ζ8 | −2ζ2−2ζ7 | −2ζ4−2ζ5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ29 | 4 | -2 | 2ζ2+2ζ7 | 2ζ4+2ζ5 | 2ζ+2ζ8 | 0 | -4 | 2 | −2ζ2−2ζ7 | −2ζ4−2ζ5 | −2ζ−2ζ8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ30 | 4 | -2 | 2ζ4+2ζ5 | 2ζ+2ζ8 | 2ζ2+2ζ7 | 0 | -4 | 2 | −2ζ4−2ζ5 | −2ζ−2ζ8 | −2ζ2−2ζ7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here ζ is a primitive root of unity of order 9 (ζ9 = 1).