Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
| 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 | C32 | C33 | C34 | C35 | C36 | C37 | C38 | C39 | C40 | C41 | C42 | C43 | C44 | C45 | C46 | C47 | C48 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 1 | 3 | 3 | 3 | 3 | 3 | 3 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 12 | 12 | 12 | 12 | 24 | 24 | 24 | 24 | 24 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 48 | 128 | 128 | 128 | 128 |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 2 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 3 | 6 | 6 | 6 |
| 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 | 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 | -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 | 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 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 |
| χ5 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | -1 | -1 | -1 | -1 |
| χ6 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | -1 | -1 | 1 | 1 |
| χ7 | 2 | -2 | 2 | 2 | -2 | -2 | -2 | 2 | 2 | -2 | 2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 0 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 |
| χ8 | 2 | -2 | 2 | 2 | -2 | -2 | -2 | 2 | 2 | -2 | 2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 0 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | ||
| χ9 | 2 | -2 | 2 | 2 | -2 | -2 | -2 | 2 | 2 | -2 | 2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 0 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | ||
| χ10 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ11 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ12 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -3 | -1 | -1 | -1 | -1 | -3 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ13 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -3 | -1 | -1 | -1 | -1 | -3 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ14 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ15 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ16 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | -3 | -1 | -1 | -1 | -1 | 1 | -3 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ17 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | -3 | -1 | -1 | -1 | -1 | 1 | -3 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ18 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ19 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | 3 | -1 | -1 | -1 | -1 | -1 | -1 | 3 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ20 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -3 | -1 | -1 | -1 | -1 | 1 | 1 | -3 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ21 | 3 | 3 | -1 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | -1 | 3 | -1 | 3 | -1 | 3 | -1 | 3 | -3 | -1 | -1 | -1 | -1 | 1 | 1 | -3 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ22 | 6 | 6 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | -2 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ23 | 6 | 6 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | -2 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ24 | 6 | 6 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ25 | 6 | 6 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ26 | 6 | 6 | -2 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | -2 | 2 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ27 | 6 | 6 | -2 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 2 | -2 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ28 | 6 | 6 | -2 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ29 | 6 | 6 | -2 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ30 | 6 | 6 | -2 | -2 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | 6 | 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 | 0 | 0 |
| χ31 | 6 | 6 | -2 | -2 | 6 | -2 | -2 | 6 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -6 | 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 | 0 | 0 |
| χ32 | 6 | -6 | 6 | 6 | -6 | -6 | -6 | 6 | 6 | -6 | -2 | -2 | 2 | 2 | -2 | -2 | 2 | 2 | 0 | -2 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ33 | 6 | -6 | 6 | -2 | 2 | -6 | 2 | -2 | -2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ34 | 6 | -6 | 6 | -2 | 2 | -6 | 2 | -2 | -2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ35 | 6 | -6 | 6 | -2 | 2 | -6 | 2 | -2 | -2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 |
| χ36 | 6 | -6 | 6 | -2 | 2 | -6 | 2 | -2 | -2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 |
| χ37 | 6 | -6 | -2 | 6 | 2 | 2 | -6 | -2 | -2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ38 | 6 | -6 | -2 | 6 | 2 | 2 | -6 | -2 | -2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ39 | 6 | -6 | -2 | 6 | 2 | 2 | -6 | -2 | -2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 |
| χ40 | 6 | -6 | -2 | 6 | 2 | 2 | -6 | -2 | -2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 |
| χ41 | 6 | -6 | -2 | -2 | -6 | 2 | 2 | 6 | -2 | 2 | 6 | -2 | -6 | 2 | 6 | -2 | -6 | 2 | 0 | -2 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ42 | 6 | -6 | -2 | -2 | -6 | 2 | 2 | 6 | -2 | 2 | -2 | 6 | 2 | -6 | -2 | 6 | 2 | -6 | 0 | -2 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ43 | 6 | -6 | -2 | -2 | -6 | 2 | 2 | 6 | -2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 2 | 2 | 0 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ44 | 6 | -6 | -2 | -2 | -6 | 2 | 2 | 6 | -2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 2 | 2 | 0 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ45 | 12 | 12 | -4 | -4 | -4 | -4 | -4 | -4 | 4 | 4 | 4 | -4 | -4 | 4 | -4 | 4 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ46 | 12 | 12 | -4 | -4 | -4 | -4 | -4 | -4 | 4 | 4 | -4 | 4 | 4 | -4 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ47 | 12 | -12 | -4 | -4 | 4 | 4 | 4 | -4 | 4 | -4 | 4 | -4 | 4 | -4 | -4 | 4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ48 | 12 | -12 | -4 | -4 | 4 | 4 | 4 | -4 | 4 | -4 | -4 | 4 | -4 | 4 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here i is the imaginary unit (i² = −1).