Finite Group DatabasebetaFinite Group DatabasebetaOrder 31200.
| 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 65 | 65 | 312 | 312 | 325 | 650 | 650 | 650 | 1200 | 1200 | 1200 | 1300 | 1300 | 1300 | 1560 | 1560 | 1950 | 1 | 65 | 65 | 312 | 312 | 325 | 650 | 650 | 650 | 1200 | 1200 | 1200 | 1300 | 1300 | 1300 | 1560 | 1560 | 1950 |
| order | 1 | 2 | 2 | 5 | 5 | 2 | 3 | 4 | 6 | 13 | 13 | 13 | 6 | 6 | 12 | 10 | 10 | 4 | 2 | 2 | 2 | 10 | 10 | 2 | 6 | 4 | 6 | 26 | 26 | 26 | 6 | 6 | 12 | 10 | 10 | 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 | 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 |
| χ3 | 13 | 1 | 5 | 3 | -2 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | 1 | -1 | -1 | 0 | 1 | -1 | 13 | 1 | 5 | 3 | -2 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | 1 | -1 | -1 | 0 | 1 | -1 |
| χ4 | 13 | 5 | 1 | -2 | 3 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | -1 | 1 | -1 | 1 | 0 | -1 | 13 | 5 | 1 | -2 | 3 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | -1 | 1 | -1 | 1 | 0 | -1 |
| χ5 | 13 | -5 | -1 | -2 | 3 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | 1 | -1 | -1 | -1 | 0 | 1 | 13 | -5 | -1 | -2 | 3 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | 1 | -1 | -1 | -1 | 0 | 1 |
| χ6 | 13 | -1 | -5 | 3 | -2 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | -1 | 1 | -1 | 0 | -1 | 1 | 13 | -1 | -5 | 3 | -2 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | -1 | 1 | -1 | 0 | -1 | 1 |
| χ7 | 25 | 5 | 5 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 0 | 0 | 1 | 25 | 5 | 5 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 0 | 0 | 1 |
| χ8 | 25 | -5 | -5 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 0 | 0 | -1 | 25 | -5 | -5 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 0 | 0 | -1 |
| χ9 | 26 | 4 | 4 | 1 | 1 | 2 | -1 | 2 | -1 | 0 | 0 | 0 | 1 | 1 | -1 | -1 | -1 | 0 | 26 | 4 | 4 | 1 | 1 | 2 | -1 | 2 | -1 | 0 | 0 | 0 | 1 | 1 | -1 | -1 | -1 | 0 |
| χ10 | 26 | 4 | -4 | 1 | 1 | 2 | -1 | -2 | -1 | 0 | 0 | 0 | 1 | -1 | 1 | 1 | -1 | 0 | 26 | 4 | -4 | 1 | 1 | 2 | -1 | -2 | -1 | 0 | 0 | 0 | 1 | -1 | 1 | 1 | -1 | 0 |
| χ11 | 26 | 6 | -6 | 1 | 1 | -2 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 | 26 | 6 | -6 | 1 | 1 | -2 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 |
| χ12 | 26 | -6 | 6 | 1 | 1 | -2 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 | 26 | -6 | 6 | 1 | 1 | -2 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 |
| χ13 | 26 | -4 | 4 | 1 | 1 | 2 | -1 | -2 | -1 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | 1 | 0 | 26 | -4 | 4 | 1 | 1 | 2 | -1 | -2 | -1 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | 1 | 0 |
| χ14 | 26 | -4 | -4 | 1 | 1 | 2 | -1 | 2 | -1 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 0 | 26 | -4 | -4 | 1 | 1 | 2 | -1 | 2 | -1 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 0 |
| χ15 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ−ζ5−ζ8−ζ12 | −ζ2−ζ3−ζ10−ζ11 | −ζ4−ζ6−ζ7−ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ−ζ5−ζ8−ζ12 | −ζ2−ζ3−ζ10−ζ11 | −ζ4−ζ6−ζ7−ζ9 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ16 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ2−ζ3−ζ10−ζ11 | −ζ4−ζ6−ζ7−ζ9 | −ζ−ζ5−ζ8−ζ12 | 0 | 0 | 0 | 0 | 0 | 0 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ2−ζ3−ζ10−ζ11 | −ζ4−ζ6−ζ7−ζ9 | −ζ−ζ5−ζ8−ζ12 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ17 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ4−ζ6−ζ7−ζ9 | −ζ−ζ5−ζ8−ζ12 | −ζ2−ζ3−ζ10−ζ11 | 0 | 0 | 0 | 0 | 0 | 0 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ4−ζ6−ζ7−ζ9 | −ζ−ζ5−ζ8−ζ12 | −ζ2−ζ3−ζ10−ζ11 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ18 | 52 | 0 | 0 | 2 | 2 | -4 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 52 | 0 | 0 | 2 | 2 | -4 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 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 | -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 | -1 | 1 | 1 | 1 |
| χ21 | 13 | 1 | 5 | 3 | -2 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | 1 | -1 | -1 | 0 | 1 | -1 | -13 | -1 | -5 | -3 | 2 | -1 | -1 | 1 | -1 | 0 | 0 | 0 | -1 | 1 | 1 | 0 | -1 | 1 |
| χ22 | 13 | 5 | 1 | -2 | 3 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | -1 | 1 | -1 | 1 | 0 | -1 | -13 | -5 | -1 | 2 | -3 | -1 | -1 | 1 | -1 | 0 | 0 | 0 | 1 | -1 | 1 | -1 | 0 | 1 |
| χ23 | 13 | -5 | -1 | -2 | 3 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | 1 | -1 | -1 | -1 | 0 | 1 | -13 | 5 | 1 | 2 | -3 | -1 | -1 | 1 | -1 | 0 | 0 | 0 | -1 | 1 | 1 | 1 | 0 | -1 |
| χ24 | 13 | -1 | -5 | 3 | -2 | 1 | 1 | -1 | 1 | 0 | 0 | 0 | -1 | 1 | -1 | 0 | -1 | 1 | -13 | 1 | 5 | -3 | 2 | -1 | -1 | 1 | -1 | 0 | 0 | 0 | 1 | -1 | 1 | 0 | 1 | -1 |
| χ25 | 25 | 5 | 5 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 0 | 0 | 1 | -25 | -5 | -5 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 0 | 0 | -1 |
| χ26 | 25 | -5 | -5 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 0 | 0 | -1 | -25 | 5 | 5 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 0 | 0 | 1 |
| χ27 | 26 | 4 | 4 | 1 | 1 | 2 | -1 | 2 | -1 | 0 | 0 | 0 | 1 | 1 | -1 | -1 | -1 | 0 | -26 | -4 | -4 | -1 | -1 | -2 | 1 | -2 | 1 | 0 | 0 | 0 | -1 | -1 | 1 | 1 | 1 | 0 |
| χ28 | 26 | 4 | -4 | 1 | 1 | 2 | -1 | -2 | -1 | 0 | 0 | 0 | 1 | -1 | 1 | 1 | -1 | 0 | -26 | -4 | 4 | -1 | -1 | -2 | 1 | 2 | 1 | 0 | 0 | 0 | -1 | 1 | -1 | -1 | 1 | 0 |
| χ29 | 26 | 6 | -6 | 1 | 1 | -2 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 | -26 | -6 | 6 | -1 | -1 | 2 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 |
| χ30 | 26 | -6 | 6 | 1 | 1 | -2 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | -1 | 0 | -26 | 6 | -6 | -1 | -1 | 2 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 0 |
| χ31 | 26 | -4 | 4 | 1 | 1 | 2 | -1 | -2 | -1 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | 1 | 0 | -26 | 4 | -4 | -1 | -1 | -2 | 1 | 2 | 1 | 0 | 0 | 0 | 1 | -1 | -1 | 1 | -1 | 0 |
| χ32 | 26 | -4 | -4 | 1 | 1 | 2 | -1 | 2 | -1 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 0 | -26 | 4 | 4 | -1 | -1 | -2 | 1 | -2 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | -1 | -1 | 0 |
| χ33 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ−ζ5−ζ8−ζ12 | −ζ2−ζ3−ζ10−ζ11 | −ζ4−ζ6−ζ7−ζ9 | 0 | 0 | 0 | 0 | 0 | 0 | -48 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | ζ+ζ5+ζ8+ζ12 | ζ2+ζ3+ζ10+ζ11 | ζ4+ζ6+ζ7+ζ9 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ34 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ2−ζ3−ζ10−ζ11 | −ζ4−ζ6−ζ7−ζ9 | −ζ−ζ5−ζ8−ζ12 | 0 | 0 | 0 | 0 | 0 | 0 | -48 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | ζ2+ζ3+ζ10+ζ11 | ζ4+ζ6+ζ7+ζ9 | ζ+ζ5+ζ8+ζ12 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ35 | 48 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | −ζ4−ζ6−ζ7−ζ9 | −ζ−ζ5−ζ8−ζ12 | −ζ2−ζ3−ζ10−ζ11 | 0 | 0 | 0 | 0 | 0 | 0 | -48 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | ζ4+ζ6+ζ7+ζ9 | ζ+ζ5+ζ8+ζ12 | ζ2+ζ3+ζ10+ζ11 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ36 | 52 | 0 | 0 | 2 | 2 | -4 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -52 | 0 | 0 | -2 | -2 | 4 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here ζ is a primitive root of unity of order 13 (ζ13 = 1).