Finite Group DatabasebetaFinite Group DatabasebetaOrder 23040.
| 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 15 | 30 | 60 | 90 | 120 | 160 | 180 | 180 | 180 | 360 | 480 | 640 | 720 | 720 | 720 | 720 | 960 | 960 | 1920 | 2304 | 1 | 15 | 30 | 60 | 90 | 120 | 160 | 180 | 180 | 180 | 360 | 480 | 640 | 720 | 720 | 720 | 720 | 960 | 960 | 1920 | 2304 |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 3 | 2 | 4 | 4 | 4 | 6 | 3 | 4 | 4 | 8 | 8 | 6 | 12 | 6 | 5 | 2 | 2 | 2 | 2 | 2 | 4 | 6 | 2 | 4 | 4 | 4 | 6 | 6 | 4 | 4 | 8 | 8 | 6 | 12 | 6 | 10 |
| 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 |
| 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 |
| χ3 | 5 | 5 | 1 | -3 | 1 | 1 | -1 | 1 | -3 | 1 | 1 | -1 | 2 | -1 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 5 | 5 | 1 | -3 | 1 | 1 | -1 | 1 | -3 | 1 | 1 | -1 | 2 | -1 | -1 | -1 | -1 | 1 | 1 | 0 | 0 |
| χ4 | 5 | 5 | 3 | -1 | 3 | 3 | 2 | 1 | -1 | 1 | 1 | 2 | -1 | -1 | 1 | -1 | 1 | 0 | 0 | -1 | 0 | 5 | 5 | 3 | -1 | 3 | 3 | 2 | 1 | -1 | 1 | 1 | 2 | -1 | -1 | 1 | -1 | 1 | 0 | 0 | -1 | 0 |
| χ5 | 5 | 5 | -3 | 1 | -3 | -3 | 2 | 1 | 1 | 1 | 1 | 2 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 1 | 0 | 5 | 5 | -3 | 1 | -3 | -3 | 2 | 1 | 1 | 1 | 1 | 2 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 1 | 0 |
| χ6 | 5 | 5 | -1 | 3 | -1 | -1 | -1 | 1 | 3 | 1 | 1 | -1 | 2 | -1 | 1 | -1 | 1 | -1 | -1 | 0 | 0 | 5 | 5 | -1 | 3 | -1 | -1 | -1 | 1 | 3 | 1 | 1 | -1 | 2 | -1 | 1 | -1 | 1 | -1 | -1 | 0 | 0 |
| χ7 | 9 | 9 | 3 | 3 | 3 | 3 | 0 | 1 | 3 | 1 | 1 | 0 | 0 | 1 | -1 | 1 | -1 | 0 | 0 | 0 | -1 | 9 | 9 | 3 | 3 | 3 | 3 | 0 | 1 | 3 | 1 | 1 | 0 | 0 | 1 | -1 | 1 | -1 | 0 | 0 | 0 | -1 |
| χ8 | 9 | 9 | -3 | -3 | -3 | -3 | 0 | 1 | -3 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | -1 | 9 | 9 | -3 | -3 | -3 | -3 | 0 | 1 | -3 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | -1 |
| χ9 | 10 | 10 | 2 | -2 | 2 | 2 | 1 | -2 | -2 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 | 10 | 10 | 2 | -2 | 2 | 2 | 1 | -2 | -2 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 |
| χ10 | 10 | 10 | -2 | 2 | -2 | -2 | 1 | -2 | 2 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 0 | 10 | 10 | -2 | 2 | -2 | -2 | 1 | -2 | 2 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 0 |
| χ11 | 15 | -1 | 5 | -3 | -3 | 1 | 3 | -1 | 1 | 3 | -1 | -1 | 0 | -1 | 1 | 1 | -1 | -1 | 1 | 0 | 0 | 15 | -1 | 5 | -3 | -3 | 1 | 3 | -1 | 1 | 3 | -1 | -1 | 0 | -1 | 1 | 1 | -1 | -1 | 1 | 0 | 0 |
| χ12 | 15 | -1 | 7 | 3 | -1 | -1 | 3 | 3 | -1 | -1 | -1 | -1 | 0 | 1 | 1 | -1 | -1 | 1 | -1 | 0 | 0 | 15 | -1 | 7 | 3 | -1 | -1 | 3 | 3 | -1 | -1 | -1 | -1 | 0 | 1 | 1 | -1 | -1 | 1 | -1 | 0 | 0 |
| χ13 | 15 | -1 | -7 | -3 | 1 | 1 | 3 | 3 | 1 | -1 | -1 | -1 | 0 | 1 | -1 | -1 | 1 | -1 | 1 | 0 | 0 | 15 | -1 | -7 | -3 | 1 | 1 | 3 | 3 | 1 | -1 | -1 | -1 | 0 | 1 | -1 | -1 | 1 | -1 | 1 | 0 | 0 |
| χ14 | 15 | -1 | -5 | 3 | 3 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | 0 | -1 | -1 | 1 | 1 | 1 | -1 | 0 | 0 | 15 | -1 | -5 | 3 | 3 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | 0 | -1 | -1 | 1 | 1 | 1 | -1 | 0 | 0 |
| χ15 | 16 | 16 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 16 | 16 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| χ16 | 30 | -2 | 2 | 6 | 2 | -2 | -3 | 2 | -2 | 2 | -2 | 1 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 | 0 | 30 | -2 | 2 | 6 | 2 | -2 | -3 | 2 | -2 | 2 | -2 | 1 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 | 0 |
| χ17 | 30 | -2 | -2 | -6 | -2 | 2 | -3 | 2 | 2 | 2 | -2 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 | 0 | 30 | -2 | -2 | -6 | -2 | 2 | -3 | 2 | 2 | 2 | -2 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 | 0 |
| χ18 | 45 | -3 | 3 | 3 | -5 | 3 | 0 | -3 | -1 | 1 | 1 | 0 | 0 | 1 | -1 | -1 | 1 | 0 | 0 | 0 | 0 | 45 | -3 | 3 | 3 | -5 | 3 | 0 | -3 | -1 | 1 | 1 | 0 | 0 | 1 | -1 | -1 | 1 | 0 | 0 | 0 | 0 |
| χ19 | 45 | -3 | 9 | -3 | 1 | -3 | 0 | 1 | 1 | -3 | 1 | 0 | 0 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | 45 | -3 | 9 | -3 | 1 | -3 | 0 | 1 | 1 | -3 | 1 | 0 | 0 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ20 | 45 | -3 | -9 | 3 | -1 | 3 | 0 | 1 | -1 | -3 | 1 | 0 | 0 | -1 | 1 | 1 | -1 | 0 | 0 | 0 | 0 | 45 | -3 | -9 | 3 | -1 | 3 | 0 | 1 | -1 | -3 | 1 | 0 | 0 | -1 | 1 | 1 | -1 | 0 | 0 | 0 | 0 |
| χ21 | 45 | -3 | -3 | -3 | 5 | -3 | 0 | -3 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | 45 | -3 | -3 | -3 | 5 | -3 | 0 | -3 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ22 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
| χ23 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 |
| χ24 | 5 | 5 | 1 | -3 | 1 | 1 | -1 | 1 | -3 | 1 | 1 | -1 | 2 | -1 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | -5 | -5 | -1 | 3 | -1 | -1 | 1 | -1 | 3 | -1 | -1 | 1 | -2 | 1 | 1 | 1 | 1 | -1 | -1 | 0 | 0 |
| χ25 | 5 | 5 | 3 | -1 | 3 | 3 | 2 | 1 | -1 | 1 | 1 | 2 | -1 | -1 | 1 | -1 | 1 | 0 | 0 | -1 | 0 | -5 | -5 | -3 | 1 | -3 | -3 | -2 | -1 | 1 | -1 | -1 | -2 | 1 | 1 | -1 | 1 | -1 | 0 | 0 | 1 | 0 |
| χ26 | 5 | 5 | -3 | 1 | -3 | -3 | 2 | 1 | 1 | 1 | 1 | 2 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 1 | 0 | -5 | -5 | 3 | -1 | 3 | 3 | -2 | -1 | -1 | -1 | -1 | -2 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | -1 | 0 |
| χ27 | 5 | 5 | -1 | 3 | -1 | -1 | -1 | 1 | 3 | 1 | 1 | -1 | 2 | -1 | 1 | -1 | 1 | -1 | -1 | 0 | 0 | -5 | -5 | 1 | -3 | 1 | 1 | 1 | -1 | -3 | -1 | -1 | 1 | -2 | 1 | -1 | 1 | -1 | 1 | 1 | 0 | 0 |
| χ28 | 9 | 9 | 3 | 3 | 3 | 3 | 0 | 1 | 3 | 1 | 1 | 0 | 0 | 1 | -1 | 1 | -1 | 0 | 0 | 0 | -1 | -9 | -9 | -3 | -3 | -3 | -3 | 0 | -1 | -3 | -1 | -1 | 0 | 0 | -1 | 1 | -1 | 1 | 0 | 0 | 0 | 1 |
| χ29 | 9 | 9 | -3 | -3 | -3 | -3 | 0 | 1 | -3 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | -1 | -9 | -9 | 3 | 3 | 3 | 3 | 0 | -1 | 3 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 1 |
| χ30 | 10 | 10 | 2 | -2 | 2 | 2 | 1 | -2 | -2 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 | -10 | -10 | -2 | 2 | -2 | -2 | -1 | 2 | 2 | 2 | 2 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 0 |
| χ31 | 10 | 10 | -2 | 2 | -2 | -2 | 1 | -2 | 2 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | -1 | 0 | -10 | -10 | 2 | -2 | 2 | 2 | -1 | 2 | -2 | 2 | 2 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 |
| χ32 | 15 | -1 | 5 | -3 | -3 | 1 | 3 | -1 | 1 | 3 | -1 | -1 | 0 | -1 | 1 | 1 | -1 | -1 | 1 | 0 | 0 | -15 | 1 | -5 | 3 | 3 | -1 | -3 | 1 | -1 | -3 | 1 | 1 | 0 | 1 | -1 | -1 | 1 | 1 | -1 | 0 | 0 |
| χ33 | 15 | -1 | 7 | 3 | -1 | -1 | 3 | 3 | -1 | -1 | -1 | -1 | 0 | 1 | 1 | -1 | -1 | 1 | -1 | 0 | 0 | -15 | 1 | -7 | -3 | 1 | 1 | -3 | -3 | 1 | 1 | 1 | 1 | 0 | -1 | -1 | 1 | 1 | -1 | 1 | 0 | 0 |
| χ34 | 15 | -1 | -7 | -3 | 1 | 1 | 3 | 3 | 1 | -1 | -1 | -1 | 0 | 1 | -1 | -1 | 1 | -1 | 1 | 0 | 0 | -15 | 1 | 7 | 3 | -1 | -1 | -3 | -3 | -1 | 1 | 1 | 1 | 0 | -1 | 1 | 1 | -1 | 1 | -1 | 0 | 0 |
| χ35 | 15 | -1 | -5 | 3 | 3 | -1 | 3 | -1 | -1 | 3 | -1 | -1 | 0 | -1 | -1 | 1 | 1 | 1 | -1 | 0 | 0 | -15 | 1 | 5 | -3 | -3 | 1 | -3 | 1 | 1 | -3 | 1 | 1 | 0 | 1 | 1 | -1 | -1 | -1 | 1 | 0 | 0 |
| χ36 | 16 | 16 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -16 | -16 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| χ37 | 30 | -2 | 2 | 6 | 2 | -2 | -3 | 2 | -2 | 2 | -2 | 1 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 | 0 | -30 | 2 | -2 | -6 | -2 | 2 | 3 | -2 | 2 | -2 | 2 | -1 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 | 0 |
| χ38 | 30 | -2 | -2 | -6 | -2 | 2 | -3 | 2 | 2 | 2 | -2 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 | 0 | -30 | 2 | 2 | 6 | 2 | -2 | 3 | -2 | -2 | -2 | 2 | -1 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 | 0 |
| χ39 | 45 | -3 | 3 | 3 | -5 | 3 | 0 | -3 | -1 | 1 | 1 | 0 | 0 | 1 | -1 | -1 | 1 | 0 | 0 | 0 | 0 | -45 | 3 | -3 | -3 | 5 | -3 | 0 | 3 | 1 | -1 | -1 | 0 | 0 | -1 | 1 | 1 | -1 | 0 | 0 | 0 | 0 |
| χ40 | 45 | -3 | 9 | -3 | 1 | -3 | 0 | 1 | 1 | -3 | 1 | 0 | 0 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | -45 | 3 | -9 | 3 | -1 | 3 | 0 | -1 | -1 | 3 | -1 | 0 | 0 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ41 | 45 | -3 | -9 | 3 | -1 | 3 | 0 | 1 | -1 | -3 | 1 | 0 | 0 | -1 | 1 | 1 | -1 | 0 | 0 | 0 | 0 | -45 | 3 | 9 | -3 | 1 | -3 | 0 | -1 | 1 | 3 | -1 | 0 | 0 | 1 | -1 | -1 | 1 | 0 | 0 | 0 | 0 |
| χ42 | 45 | -3 | -3 | -3 | 5 | -3 | 0 | -3 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | -45 | 3 | 3 | 3 | -5 | 3 | 0 | 3 | -1 | -1 | -1 | 0 | 0 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 |