Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
| 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 | C31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 1 | 2 | 6 | 6 | 8 | 8 | 12 | 12 | 12 | 12 | 12 | 12 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 24 | 32 | 32 | 48 | 48 | 48 | 48 | 64 | 64 | 64 |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 6 | 4 | 4 | 8 | 8 | 6 | 6 | 12 |
| 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 | 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 | 1 |
| χ3 | 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 | -1 |
| χ4 | 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 | -1 |
| χ5 | 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 | -1 |
| χ6 | 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 | -1 |
| 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 | 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 | 1 |
| χ9 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 |
| χ10 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | 2 | 2 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | 1 | 1 |
| χ11 | 2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | -1 | 1 |
| χ12 | 2 | 2 | -2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | 1 | -1 |
| χ13 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 0 | 0 | -1 | -1 | -1 | -1 | 0 | 0 | 0 |
| χ14 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
| χ15 | 3 | 3 | 3 | 3 | 3 | -3 | -3 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 0 | 0 | 1 | 1 | -1 | -1 | 0 | 0 | 0 |
| χ16 | 3 | 3 | 3 | 3 | 3 | -3 | -3 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | 0 | 0 | -1 | -1 | 1 | 1 | 0 | 0 | 0 |
| χ17 | 3 | 3 | -3 | -3 | 3 | 3 | -3 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 0 | 0 | -1 | 1 | -1 | 1 | 0 | 0 | 0 |
| χ18 | 3 | 3 | -3 | -3 | 3 | 3 | -3 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 0 | 0 | 1 | -1 | 1 | -1 | 0 | 0 | 0 |
| χ19 | 3 | 3 | -3 | -3 | 3 | -3 | 3 | 1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | 1 | 0 | 0 | 1 | -1 | -1 | 1 | 0 | 0 | 0 |
| χ20 | 3 | 3 | -3 | -3 | 3 | -3 | 3 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 0 | 0 | -1 | 1 | 1 | -1 | 0 | 0 | 0 |
| χ21 | 6 | 6 | 6 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | -2 | 2 | 0 | 0 | 2 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ22 | 6 | 6 | 6 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | -2 | -2 | 0 | 0 | -2 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ23 | 6 | 6 | 6 | -2 | -2 | 0 | 0 | -2 | -2 | 2 | 2 | 2 | 2 | 0 | -2 | -2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ24 | 6 | 6 | 6 | -2 | -2 | 0 | 0 | -2 | -2 | 2 | -2 | -2 | 2 | 0 | 2 | 2 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ25 | 6 | 6 | -6 | 2 | -2 | 0 | 0 | 2 | -2 | -2 | 2 | 2 | 2 | 0 | -2 | 2 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ26 | 6 | 6 | -6 | 2 | -2 | 0 | 0 | 2 | -2 | -2 | -2 | -2 | 2 | 0 | 2 | -2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ27 | 6 | 6 | -6 | 2 | -2 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | -2 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ28 | 6 | 6 | -6 | 2 | -2 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | -2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ29 | 8 | -8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| χ30 | 8 | -8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| χ31 | 16 | -16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here i is the imaginary unit (i² = −1).