Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
| 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 8 | 8 | 8 | 25 | 50 | 50 | 50 | 1 | 8 | 8 | 8 | 25 | 50 | 50 | 50 | 1 | 8 | 8 | 8 | 25 | 50 | 50 | 50 | 1 | 8 | 8 | 8 | 25 | 50 | 50 | 50 |
| order | 1 | 5 | 5 | 5 | 2 | 4 | 4 | 4 | 2 | 10 | 10 | 10 | 2 | 4 | 4 | 4 | 2 | 10 | 10 | 10 | 2 | 4 | 4 | 4 | 2 | 10 | 10 | 10 | 2 | 4 | 4 | 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 | 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 |
| 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 |
| 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 |
| χ5 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 |
| χ6 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 |
| χ7 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 |
| χ8 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 |
| χ9 | 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 |
| χ10 | 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 |
| χ11 | 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 |
| χ12 | 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 |
| χ13 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 |
| χ14 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | -8 | -3 | 2 | 2 | 0 | 0 | 0 | 0 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | -8 | -3 | 2 | 2 | 0 | 0 | 0 | 0 |
| χ15 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | -8 | 2 | -3 | 2 | 0 | 0 | 0 | 0 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | -8 | 2 | -3 | 2 | 0 | 0 | 0 | 0 |
| χ16 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | -8 | 2 | 2 | -3 | 0 | 0 | 0 | 0 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | -8 | 2 | 2 | -3 | 0 | 0 | 0 | 0 |
| χ17 | 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 |
| χ18 | 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 |
| 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 | -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 | 1 | -1 |
| χ21 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 |
| χ22 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | -8 | -3 | 2 | 2 | 0 | 0 | 0 | 0 | -8 | -3 | 2 | 2 | 0 | 0 | 0 | 0 |
| χ23 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | -8 | 2 | -3 | 2 | 0 | 0 | 0 | 0 | -8 | 2 | -3 | 2 | 0 | 0 | 0 | 0 |
| χ24 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | -8 | 2 | 2 | -3 | 0 | 0 | 0 | 0 | -8 | 2 | 2 | -3 | 0 | 0 | 0 | 0 |
| χ25 | 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 |
| χ26 | 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 |
| χ27 | 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 |
| χ28 | 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 |
| χ29 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 0 |
| χ30 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 | -8 | -3 | 2 | 2 | 0 | 0 | 0 | 0 | -8 | -3 | 2 | 2 | 0 | 0 | 0 | 0 | 8 | 3 | -2 | -2 | 0 | 0 | 0 | 0 |
| χ31 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 | -8 | 2 | -3 | 2 | 0 | 0 | 0 | 0 | -8 | 2 | -3 | 2 | 0 | 0 | 0 | 0 | 8 | -2 | 3 | -2 | 0 | 0 | 0 | 0 |
| χ32 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 | -8 | 2 | 2 | -3 | 0 | 0 | 0 | 0 | -8 | 2 | 2 | -3 | 0 | 0 | 0 | 0 | 8 | -2 | -2 | 3 | 0 | 0 | 0 | 0 |