Order 224.
| 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 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | 14 | 14 | 14 | 56 |
| order | 1 | 2 | 4 | 7 | 7 | 7 | 8 | 8 | 14 | 14 | 14 | 28 | 28 | 28 | 56 | 56 | 56 | 56 | 56 | 56 | 4 | 28 | 28 | 28 | 28 | 28 | 28 | 16 | 16 | 16 | 16 | 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 | 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 |
| χ6 | 2 | 2 | 2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | 2 | 2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | 2 | −ζ40−ζ72 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | 0 | 0 | 0 | 0 | 0 |
| χ7 | 2 | 2 | 2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | 2 | 2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | -2 | ζ40+ζ72 | ζ40+ζ72 | ζ24+ζ88 | ζ24+ζ88 | ζ8+ζ104 | ζ8+ζ104 | 0 | 0 | 0 | 0 | 0 |
| χ8 | 2 | 2 | 2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | -2 | -2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | ζ40+ζ72 | ζ40+ζ72 | ζ24+ζ88 | ζ24+ζ88 | ζ8+ζ104 | ζ8+ζ104 | 0 | ζ40−ζ72 | −ζ40+ζ72 | ζ24−ζ88 | −ζ24+ζ88 | −ζ8+ζ104 | ζ8−ζ104 | 0 | 0 | 0 | 0 | 0 |
| χ9 | 2 | 2 | 2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | -2 | -2 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | ζ40+ζ72 | ζ40+ζ72 | ζ24+ζ88 | ζ24+ζ88 | ζ8+ζ104 | ζ8+ζ104 | 0 | −ζ40+ζ72 | ζ40−ζ72 | −ζ24+ζ88 | ζ24−ζ88 | ζ8−ζ104 | −ζ8+ζ104 | 0 | 0 | 0 | 0 | 0 |
| χ10 | 2 | 2 | 2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | 2 | 2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | 2 | −ζ24−ζ88 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | 0 | 0 | 0 | 0 | 0 |
| χ11 | 2 | 2 | 2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | 2 | 2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | -2 | ζ24+ζ88 | ζ24+ζ88 | ζ8+ζ104 | ζ8+ζ104 | ζ40+ζ72 | ζ40+ζ72 | 0 | 0 | 0 | 0 | 0 |
| χ12 | 2 | 2 | 2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | -2 | -2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | ζ24+ζ88 | ζ24+ζ88 | ζ8+ζ104 | ζ8+ζ104 | ζ40+ζ72 | ζ40+ζ72 | 0 | ζ24−ζ88 | −ζ24+ζ88 | −ζ8+ζ104 | ζ8−ζ104 | ζ40−ζ72 | −ζ40+ζ72 | 0 | 0 | 0 | 0 | 0 |
| χ13 | 2 | 2 | 2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | -2 | -2 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | ζ24+ζ88 | ζ24+ζ88 | ζ8+ζ104 | ζ8+ζ104 | ζ40+ζ72 | ζ40+ζ72 | 0 | −ζ24+ζ88 | ζ24−ζ88 | ζ8−ζ104 | −ζ8+ζ104 | −ζ40+ζ72 | ζ40−ζ72 | 0 | 0 | 0 | 0 | 0 |
| χ14 | 2 | 2 | 2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | 2 | 2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | 2 | −ζ8−ζ104 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | 0 | 0 | 0 | 0 | 0 |
| χ15 | 2 | 2 | 2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | 2 | 2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ24−ζ88 | -2 | ζ8+ζ104 | ζ8+ζ104 | ζ40+ζ72 | ζ40+ζ72 | ζ24+ζ88 | ζ24+ζ88 | 0 | 0 | 0 | 0 | 0 |
| χ16 | 2 | 2 | 2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | -2 | -2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | ζ8+ζ104 | ζ8+ζ104 | ζ40+ζ72 | ζ40+ζ72 | ζ24+ζ88 | ζ24+ζ88 | 0 | −ζ8+ζ104 | ζ8−ζ104 | ζ40−ζ72 | −ζ40+ζ72 | ζ24−ζ88 | −ζ24+ζ88 | 0 | 0 | 0 | 0 | 0 |
| χ17 | 2 | 2 | 2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | -2 | -2 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | −ζ8−ζ104 | −ζ40−ζ72 | −ζ24−ζ88 | ζ8+ζ104 | ζ8+ζ104 | ζ40+ζ72 | ζ40+ζ72 | ζ24+ζ88 | ζ24+ζ88 | 0 | ζ8−ζ104 | −ζ8+ζ104 | −ζ40+ζ72 | ζ40−ζ72 | −ζ24+ζ88 | ζ24−ζ88 | 0 | 0 | 0 | 0 | 0 |
| χ18 | 2 | 2 | -2 | 2 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ19 | 2 | 2 | -2 | 2 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ20 | 2 | -2 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ11+ζ13+ζ27+ζ29+ζ43+ζ45+ζ59+ζ61+ζ75+ζ93+ζ107+ζ109 | −ζ11−ζ13−ζ27−ζ29−ζ43−ζ45−ζ59−ζ61−ζ75−ζ93−ζ107−ζ109 | −ζ9−ζ15−ζ25−ζ31−ζ41−ζ47−ζ57−ζ73−ζ79−ζ89−ζ95−ζ111 | ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ111 | 0 | ||||||||
| χ21 | 2 | -2 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | −ζ11−ζ13−ζ27−ζ29−ζ43−ζ45−ζ59−ζ61−ζ75−ζ93−ζ107−ζ109 | ζ11+ζ13+ζ27+ζ29+ζ43+ζ45+ζ59+ζ61+ζ75+ζ93+ζ107+ζ109 | ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ111 | −ζ9−ζ15−ζ25−ζ31−ζ41−ζ47−ζ57−ζ73−ζ79−ζ89−ζ95−ζ111 | 0 | ||||||||
| χ22 | 2 | -2 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | −ζ9−ζ15−ζ25−ζ31−ζ41−ζ47−ζ57−ζ73−ζ79−ζ89−ζ95−ζ111 | ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ111 | −ζ11−ζ13−ζ27−ζ29−ζ43−ζ45−ζ59−ζ61−ζ75−ζ93−ζ107−ζ109 | ζ11+ζ13+ζ27+ζ29+ζ43+ζ45+ζ59+ζ61+ζ75+ζ93+ζ107+ζ109 | 0 | ||||||||
| χ23 | 2 | -2 | 0 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ111 | −ζ9−ζ15−ζ25−ζ31−ζ41−ζ47−ζ57−ζ73−ζ79−ζ89−ζ95−ζ111 | ζ11+ζ13+ζ27+ζ29+ζ43+ζ45+ζ59+ζ61+ζ75+ζ93+ζ107+ζ109 | −ζ11−ζ13−ζ27−ζ29−ζ43−ζ45−ζ59−ζ61−ζ75−ζ93−ζ107−ζ109 | 0 | ||||||||
| χ24 | 4 | 4 | -4 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | 0 | 0 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | 2ζ40+2ζ72 | 2ζ24+2ζ88 | 2ζ8+2ζ104 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ25 | 4 | 4 | -4 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | 0 | 0 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | 2ζ24+2ζ88 | 2ζ8+2ζ104 | 2ζ40+2ζ72 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ26 | 4 | 4 | -4 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | 0 | 0 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | 2ζ8+2ζ104 | 2ζ40+2ζ72 | 2ζ24+2ζ88 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ27 | 4 | -4 | 0 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | 2ζ40+2ζ72 | 2ζ24+2ζ88 | 2ζ8+2ζ104 | 0 | 0 | 0 | −ζ26+ζ30−ζ58+ζ110 | ζ26−ζ30+ζ58−ζ110 | −ζ10+ζ46−ζ74+ζ94 | ζ10−ζ46+ζ74−ζ94 | ζ62+ζ78−ζ90−ζ106 | −ζ62−ζ78+ζ90+ζ106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| χ28 | 4 | -4 | 0 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | 2ζ40+2ζ72 | 2ζ24+2ζ88 | 2ζ8+2ζ104 | 0 | 0 | 0 | ζ26−ζ30+ζ58−ζ110 | −ζ26+ζ30−ζ58+ζ110 | ζ10−ζ46+ζ74−ζ94 | −ζ10+ζ46−ζ74+ζ94 | −ζ62−ζ78+ζ90+ζ106 | ζ62+ζ78−ζ90−ζ106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| χ29 | 4 | -4 | 0 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | 2ζ24+2ζ88 | 2ζ8+2ζ104 | 2ζ40+2ζ72 | 0 | 0 | 0 | −ζ10+ζ46−ζ74+ζ94 | ζ10−ζ46+ζ74−ζ94 | ζ62+ζ78−ζ90−ζ106 | −ζ62−ζ78+ζ90+ζ106 | −ζ26+ζ30−ζ58+ζ110 | ζ26−ζ30+ζ58−ζ110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| χ30 | 4 | -4 | 0 | −2ζ24−2ζ88 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | 2ζ24+2ζ88 | 2ζ8+2ζ104 | 2ζ40+2ζ72 | 0 | 0 | 0 | ζ10−ζ46+ζ74−ζ94 | −ζ10+ζ46−ζ74+ζ94 | −ζ62−ζ78+ζ90+ζ106 | ζ62+ζ78−ζ90−ζ106 | ζ26−ζ30+ζ58−ζ110 | −ζ26+ζ30−ζ58+ζ110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| χ31 | 4 | -4 | 0 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | 2ζ8+2ζ104 | 2ζ40+2ζ72 | 2ζ24+2ζ88 | 0 | 0 | 0 | ζ62+ζ78−ζ90−ζ106 | −ζ62−ζ78+ζ90+ζ106 | −ζ26+ζ30−ζ58+ζ110 | ζ26−ζ30+ζ58−ζ110 | −ζ10+ζ46−ζ74+ζ94 | ζ10−ζ46+ζ74−ζ94 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| χ32 | 4 | -4 | 0 | −2ζ8−2ζ104 | −2ζ40−2ζ72 | −2ζ24−2ζ88 | 2ζ8+2ζ104 | 2ζ40+2ζ72 | 2ζ24+2ζ88 | 0 | 0 | 0 | −ζ62−ζ78+ζ90+ζ106 | ζ62+ζ78−ζ90−ζ106 | ζ26−ζ30+ζ58−ζ110 | −ζ26+ζ30−ζ58+ζ110 | ζ10−ζ46+ζ74−ζ94 | −ζ10+ζ46−ζ74+ζ94 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here ζ is a primitive root of unity of order 112 (ζ112 = 1).