Order 176.
| 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 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 22 | 22 | 44 |
| order | 1 | 2 | 4 | 11 | 11 | 11 | 11 | 11 | 22 | 22 | 22 | 22 | 22 | 4 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 44 | 8 | 8 | 2 |
| 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 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | 2 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ4−ζ84 | 0 | 0 | 0 |
| χ6 | 2 | 2 | 2 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | -2 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | ζ36+ζ52 | ζ36+ζ52 | ζ12+ζ76 | ζ12+ζ76 | ζ28+ζ60 | ζ28+ζ60 | ζ20+ζ68 | ζ20+ζ68 | ζ4+ζ84 | ζ4+ζ84 | 0 | 0 | 0 |
| χ7 | 2 | 2 | 2 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | 2 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ28−ζ60 | 0 | 0 | 0 |
| χ8 | 2 | 2 | 2 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | -2 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | ζ12+ζ76 | ζ12+ζ76 | ζ4+ζ84 | ζ4+ζ84 | ζ20+ζ68 | ζ20+ζ68 | ζ36+ζ52 | ζ36+ζ52 | ζ28+ζ60 | ζ28+ζ60 | 0 | 0 | 0 |
| χ9 | 2 | 2 | 2 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | 2 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ36−ζ52 | 0 | 0 | 0 |
| χ10 | 2 | 2 | 2 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | -2 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | ζ28+ζ60 | ζ28+ζ60 | ζ20+ζ68 | ζ20+ζ68 | ζ12+ζ76 | ζ12+ζ76 | ζ4+ζ84 | ζ4+ζ84 | ζ36+ζ52 | ζ36+ζ52 | 0 | 0 | 0 |
| χ11 | 2 | 2 | 2 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | 2 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ12−ζ76 | 0 | 0 | 0 |
| χ12 | 2 | 2 | 2 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | -2 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | ζ20+ζ68 | ζ20+ζ68 | ζ36+ζ52 | ζ36+ζ52 | ζ4+ζ84 | ζ4+ζ84 | ζ28+ζ60 | ζ28+ζ60 | ζ12+ζ76 | ζ12+ζ76 | 0 | 0 | 0 |
| χ13 | 2 | 2 | 2 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | 2 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ20−ζ68 | 0 | 0 | 0 |
| χ14 | 2 | 2 | 2 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | -2 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | ζ4+ζ84 | ζ4+ζ84 | ζ28+ζ60 | ζ28+ζ60 | ζ36+ζ52 | ζ36+ζ52 | ζ12+ζ76 | ζ12+ζ76 | ζ20+ζ68 | ζ20+ζ68 | 0 | 0 | 0 |
| χ15 | 2 | 2 | -2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | -2 | -2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ16 | 2 | 2 | -2 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | 0 | ζ36+ζ52 | ζ12+ζ76 | ζ28+ζ60 | ζ20+ζ68 | ζ4+ζ84 | ζ36−ζ52 | −ζ36+ζ52 | ζ12−ζ76 | −ζ12+ζ76 | ζ28−ζ60 | −ζ28+ζ60 | ζ20−ζ68 | −ζ20+ζ68 | −ζ4+ζ84 | ζ4−ζ84 | 0 | 0 | 0 |
| χ17 | 2 | 2 | -2 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ4−ζ84 | 0 | ζ36+ζ52 | ζ12+ζ76 | ζ28+ζ60 | ζ20+ζ68 | ζ4+ζ84 | −ζ36+ζ52 | ζ36−ζ52 | −ζ12+ζ76 | ζ12−ζ76 | −ζ28+ζ60 | ζ28−ζ60 | −ζ20+ζ68 | ζ20−ζ68 | ζ4−ζ84 | −ζ4+ζ84 | 0 | 0 | 0 |
| χ18 | 2 | 2 | -2 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | 0 | ζ12+ζ76 | ζ4+ζ84 | ζ20+ζ68 | ζ36+ζ52 | ζ28+ζ60 | ζ12−ζ76 | −ζ12+ζ76 | ζ4−ζ84 | −ζ4+ζ84 | −ζ20+ζ68 | ζ20−ζ68 | ζ36−ζ52 | −ζ36+ζ52 | ζ28−ζ60 | −ζ28+ζ60 | 0 | 0 | 0 |
| χ19 | 2 | 2 | -2 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ28−ζ60 | 0 | ζ12+ζ76 | ζ4+ζ84 | ζ20+ζ68 | ζ36+ζ52 | ζ28+ζ60 | −ζ12+ζ76 | ζ12−ζ76 | −ζ4+ζ84 | ζ4−ζ84 | ζ20−ζ68 | −ζ20+ζ68 | −ζ36+ζ52 | ζ36−ζ52 | −ζ28+ζ60 | ζ28−ζ60 | 0 | 0 | 0 |
| χ20 | 2 | 2 | -2 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | 0 | ζ28+ζ60 | ζ20+ζ68 | ζ12+ζ76 | ζ4+ζ84 | ζ36+ζ52 | ζ28−ζ60 | −ζ28+ζ60 | −ζ20+ζ68 | ζ20−ζ68 | ζ12−ζ76 | −ζ12+ζ76 | −ζ4+ζ84 | ζ4−ζ84 | ζ36−ζ52 | −ζ36+ζ52 | 0 | 0 | 0 |
| χ21 | 2 | 2 | -2 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | −ζ28−ζ60 | −ζ20−ζ68 | −ζ12−ζ76 | −ζ4−ζ84 | −ζ36−ζ52 | 0 | ζ28+ζ60 | ζ20+ζ68 | ζ12+ζ76 | ζ4+ζ84 | ζ36+ζ52 | −ζ28+ζ60 | ζ28−ζ60 | ζ20−ζ68 | −ζ20+ζ68 | −ζ12+ζ76 | ζ12−ζ76 | ζ4−ζ84 | −ζ4+ζ84 | −ζ36+ζ52 | ζ36−ζ52 | 0 | 0 | 0 |
| χ22 | 2 | 2 | -2 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | 0 | ζ20+ζ68 | ζ36+ζ52 | ζ4+ζ84 | ζ28+ζ60 | ζ12+ζ76 | ζ20−ζ68 | −ζ20+ζ68 | ζ36−ζ52 | −ζ36+ζ52 | −ζ4+ζ84 | ζ4−ζ84 | −ζ28+ζ60 | ζ28−ζ60 | −ζ12+ζ76 | ζ12−ζ76 | 0 | 0 | 0 |
| χ23 | 2 | 2 | -2 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ36−ζ52 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ12−ζ76 | 0 | ζ20+ζ68 | ζ36+ζ52 | ζ4+ζ84 | ζ28+ζ60 | ζ12+ζ76 | −ζ20+ζ68 | ζ20−ζ68 | −ζ36+ζ52 | ζ36−ζ52 | ζ4−ζ84 | −ζ4+ζ84 | ζ28−ζ60 | −ζ28+ζ60 | ζ12−ζ76 | −ζ12+ζ76 | 0 | 0 | 0 |
| χ24 | 2 | 2 | -2 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | 0 | ζ4+ζ84 | ζ28+ζ60 | ζ36+ζ52 | ζ12+ζ76 | ζ20+ζ68 | −ζ4+ζ84 | ζ4−ζ84 | ζ28−ζ60 | −ζ28+ζ60 | ζ36−ζ52 | −ζ36+ζ52 | −ζ12+ζ76 | ζ12−ζ76 | ζ20−ζ68 | −ζ20+ζ68 | 0 | 0 | 0 |
| χ25 | 2 | 2 | -2 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | −ζ4−ζ84 | −ζ28−ζ60 | −ζ36−ζ52 | −ζ12−ζ76 | −ζ20−ζ68 | 0 | ζ4+ζ84 | ζ28+ζ60 | ζ36+ζ52 | ζ12+ζ76 | ζ20+ζ68 | ζ4−ζ84 | −ζ4+ζ84 | −ζ28+ζ60 | ζ28−ζ60 | −ζ36+ζ52 | ζ36−ζ52 | ζ12−ζ76 | −ζ12+ζ76 | −ζ20+ζ68 | ζ20−ζ68 | 0 | 0 | 0 |
| χ26 | 2 | -2 | 0 | 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 | 0 | ||
| χ27 | 2 | -2 | 0 | 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 | 0 | ||
| χ28 | 4 | -4 | 0 | −2ζ36−2ζ52 | −2ζ12−2ζ76 | −2ζ28−2ζ60 | −2ζ20−2ζ68 | −2ζ4−2ζ84 | 2ζ36+2ζ52 | 2ζ12+2ζ76 | 2ζ28+2ζ60 | 2ζ20+2ζ68 | 2ζ4+2ζ84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ29 | 4 | -4 | 0 | −2ζ12−2ζ76 | −2ζ4−2ζ84 | −2ζ20−2ζ68 | −2ζ36−2ζ52 | −2ζ28−2ζ60 | 2ζ12+2ζ76 | 2ζ4+2ζ84 | 2ζ20+2ζ68 | 2ζ36+2ζ52 | 2ζ28+2ζ60 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ30 | 4 | -4 | 0 | −2ζ28−2ζ60 | −2ζ20−2ζ68 | −2ζ12−2ζ76 | −2ζ4−2ζ84 | −2ζ36−2ζ52 | 2ζ28+2ζ60 | 2ζ20+2ζ68 | 2ζ12+2ζ76 | 2ζ4+2ζ84 | 2ζ36+2ζ52 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ31 | 4 | -4 | 0 | −2ζ20−2ζ68 | −2ζ36−2ζ52 | −2ζ4−2ζ84 | −2ζ28−2ζ60 | −2ζ12−2ζ76 | 2ζ20+2ζ68 | 2ζ36+2ζ52 | 2ζ4+2ζ84 | 2ζ28+2ζ60 | 2ζ12+2ζ76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ32 | 4 | -4 | 0 | −2ζ4−2ζ84 | −2ζ28−2ζ60 | −2ζ36−2ζ52 | −2ζ12−2ζ76 | −2ζ20−2ζ68 | 2ζ4+2ζ84 | 2ζ28+2ζ60 | 2ζ36+2ζ52 | 2ζ12+2ζ76 | 2ζ20+2ζ68 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here ζ is a primitive root of unity of order 88 (ζ88 = 1); i = ζ22.