Finite Group Databasebeta

← Group #6402

Character table — Group #6402

Order 224.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size1122222222244444444488888881414141456
order124777881414142828285656565656564282828282828161616162
χ111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-11111-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-11
χ5222222-2-2222222-2-2-2-2-2-2000000000000
χ6222−ζ40−ζ72−ζ24−ζ88−ζ8−ζ10422−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ40−ζ72−ζ24−ζ88−ζ24−ζ88−ζ8−ζ104−ζ8−ζ1042−ζ40−ζ72−ζ40−ζ72−ζ24−ζ88−ζ24−ζ88−ζ8−ζ104−ζ8−ζ10400000
χ7222−ζ40−ζ72−ζ24−ζ88−ζ8−ζ10422−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ40−ζ72−ζ24−ζ88−ζ24−ζ88−ζ8−ζ104−ζ8−ζ104-2ζ40+ζ72ζ40+ζ72ζ24+ζ88ζ24+ζ88ζ8+ζ104ζ8+ζ10400000
χ8222−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104-2-2−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104ζ40+ζ72ζ40+ζ72ζ24+ζ88ζ24+ζ88ζ8+ζ104ζ8+ζ1040ζ40−ζ72−ζ40+ζ72ζ24−ζ88−ζ24+ζ88−ζ8+ζ104ζ8−ζ10400000
χ9222−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104-2-2−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104ζ40+ζ72ζ40+ζ72ζ24+ζ88ζ24+ζ88ζ8+ζ104ζ8+ζ1040−ζ40+ζ72ζ40−ζ72−ζ24+ζ88ζ24−ζ88ζ8−ζ104−ζ8+ζ10400000
χ10222−ζ24−ζ88−ζ8−ζ104−ζ40−ζ7222−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ24−ζ88−ζ8−ζ104−ζ8−ζ104−ζ40−ζ72−ζ40−ζ722−ζ24−ζ88−ζ24−ζ88−ζ8−ζ104−ζ8−ζ104−ζ40−ζ72−ζ40−ζ7200000
χ11222−ζ24−ζ88−ζ8−ζ104−ζ40−ζ7222−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ24−ζ88−ζ8−ζ104−ζ8−ζ104−ζ40−ζ72−ζ40−ζ72-2ζ24+ζ88ζ24+ζ88ζ8+ζ104ζ8+ζ104ζ40+ζ72ζ40+ζ7200000
χ12222−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72-2-2−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72ζ24+ζ88ζ24+ζ88ζ8+ζ104ζ8+ζ104ζ40+ζ72ζ40+ζ720ζ24−ζ88−ζ24+ζ88−ζ8+ζ104ζ8−ζ104ζ40−ζ72−ζ40+ζ7200000
χ13222−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72-2-2−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72ζ24+ζ88ζ24+ζ88ζ8+ζ104ζ8+ζ104ζ40+ζ72ζ40+ζ720−ζ24+ζ88ζ24−ζ88ζ8−ζ104−ζ8+ζ104−ζ40+ζ72ζ40−ζ7200000
χ14222−ζ8−ζ104−ζ40−ζ72−ζ24−ζ8822−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ8−ζ104−ζ40−ζ72−ζ40−ζ72−ζ24−ζ88−ζ24−ζ882−ζ8−ζ104−ζ8−ζ104−ζ40−ζ72−ζ40−ζ72−ζ24−ζ88−ζ24−ζ8800000
χ15222−ζ8−ζ104−ζ40−ζ72−ζ24−ζ8822−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ8−ζ104−ζ40−ζ72−ζ40−ζ72−ζ24−ζ88−ζ24−ζ88-2ζ8+ζ104ζ8+ζ104ζ40+ζ72ζ40+ζ72ζ24+ζ88ζ24+ζ8800000
χ16222−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88-2-2−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88ζ8+ζ104ζ8+ζ104ζ40+ζ72ζ40+ζ72ζ24+ζ88ζ24+ζ880−ζ8+ζ104ζ8−ζ104ζ40−ζ72−ζ40+ζ72ζ24−ζ88−ζ24+ζ8800000
χ17222−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88-2-2−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88−ζ8−ζ104−ζ40−ζ72−ζ24−ζ88ζ8+ζ104ζ8+ζ104ζ40+ζ72ζ40+ζ72ζ24+ζ88ζ24+ζ880ζ8−ζ104−ζ8+ζ104−ζ40+ζ72ζ40−ζ72−ζ24+ζ88ζ24−ζ8800000
χ1822-222200222-2-2-2000000000000022−2−20
χ1922-222200222-2-2-20000000000000−2−2220
χ202-202222−2-2-2-20002−22−22−20000000ζ11+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−ζ111ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ1110
χ212-202222−2-2-2-20002−22−22−20000000−ζ11−ζ13−ζ27−ζ29−ζ43−ζ45−ζ59−ζ61−ζ75−ζ93−ζ107−ζ109ζ11+ζ13+ζ27+ζ29+ζ43+ζ45+ζ59+ζ61+ζ75+ζ93+ζ107+ζ109ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ111−ζ9−ζ15−ζ25−ζ31−ζ41−ζ47−ζ57−ζ73−ζ79−ζ89−ζ95−ζ1110
χ222-20222−22-2-2-2000−22−22−220000000−ζ9−ζ15−ζ25−ζ31−ζ41−ζ47−ζ57−ζ73−ζ79−ζ89−ζ95−ζ111ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ111−ζ11−ζ13−ζ27−ζ29−ζ43−ζ45−ζ59−ζ61−ζ75−ζ93−ζ107−ζ109ζ11+ζ13+ζ27+ζ29+ζ43+ζ45+ζ59+ζ61+ζ75+ζ93+ζ107+ζ1090
χ232-20222−22-2-2-2000−22−22−220000000ζ9+ζ15+ζ25+ζ31+ζ41+ζ47+ζ57+ζ73+ζ79+ζ89+ζ95+ζ111−ζ9−ζ15−ζ25−ζ31−ζ41−ζ47−ζ57−ζ73−ζ79−ζ89−ζ95−ζ111ζ11+ζ13+ζ27+ζ29+ζ43+ζ45+ζ59+ζ61+ζ75+ζ93+ζ107+ζ109−ζ11−ζ13−ζ27−ζ29−ζ43−ζ45−ζ59−ζ61−ζ75−ζ93−ζ107−ζ1090
χ2444-4−2ζ40−2ζ72−2ζ24−2ζ88−2ζ8−2ζ10400−2ζ40−2ζ72−2ζ24−2ζ88−2ζ8−2ζ1042ζ40+2ζ722ζ24+2ζ882ζ8+2ζ104000000000000000000
χ2544-4−2ζ24−2ζ88−2ζ8−2ζ104−2ζ40−2ζ7200−2ζ24−2ζ88−2ζ8−2ζ104−2ζ40−2ζ722ζ24+2ζ882ζ8+2ζ1042ζ40+2ζ72000000000000000000
χ2644-4−2ζ8−2ζ104−2ζ40−2ζ72−2ζ24−2ζ8800−2ζ8−2ζ104−2ζ40−2ζ72−2ζ24−2ζ882ζ8+2ζ1042ζ40+2ζ722ζ24+2ζ88000000000000000000
χ274-40−2ζ40−2ζ72−2ζ24−2ζ88−2ζ8−2ζ10422−222ζ40+2ζ722ζ24+2ζ882ζ8+2ζ104000−ζ26+ζ30−ζ58+ζ110ζ26−ζ30+ζ58−ζ110−ζ10+ζ46−ζ74+ζ94ζ10−ζ46+ζ74−ζ94ζ62+ζ78−ζ90−ζ106−ζ62−ζ78+ζ90+ζ106000000000000
χ284-40−2ζ40−2ζ72−2ζ24−2ζ88−2ζ8−2ζ104−22222ζ40+2ζ722ζ24+2ζ882ζ8+2ζ104000ζ26−ζ30+ζ58−ζ110−ζ26+ζ30−ζ58+ζ110ζ10−ζ46+ζ74−ζ94−ζ10+ζ46−ζ74+ζ94−ζ62−ζ78+ζ90+ζ106ζ62+ζ78−ζ90−ζ106000000000000
χ294-40−2ζ24−2ζ88−2ζ8−2ζ104−2ζ40−2ζ7222−222ζ24+2ζ882ζ8+2ζ1042ζ40+2ζ72000−ζ10+ζ46−ζ74+ζ94ζ10−ζ46+ζ74−ζ94ζ62+ζ78−ζ90−ζ106−ζ62−ζ78+ζ90+ζ106−ζ26+ζ30−ζ58+ζ110ζ26−ζ30+ζ58−ζ110000000000000
χ304-40−2ζ24−2ζ88−2ζ8−2ζ104−2ζ40−2ζ72−22222ζ24+2ζ882ζ8+2ζ1042ζ40+2ζ72000ζ10−ζ46+ζ74−ζ94−ζ10+ζ46−ζ74+ζ94−ζ62−ζ78+ζ90+ζ106ζ62+ζ78−ζ90−ζ106ζ26−ζ30+ζ58−ζ110−ζ26+ζ30−ζ58+ζ110000000000000
χ314-40−2ζ8−2ζ104−2ζ40−2ζ72−2ζ24−2ζ8822−222ζ8+2ζ1042ζ40+2ζ722ζ24+2ζ88000ζ62+ζ78−ζ90−ζ106−ζ62−ζ78+ζ90+ζ106−ζ26+ζ30−ζ58+ζ110ζ26−ζ30+ζ58−ζ110−ζ10+ζ46−ζ74+ζ94ζ10−ζ46+ζ74−ζ94000000000000
χ324-40−2ζ8−2ζ104−2ζ40−2ζ72−2ζ24−2ζ88−22222ζ8+2ζ1042ζ40+2ζ722ζ24+2ζ88000−ζ62−ζ78+ζ90+ζ106ζ62+ζ78−ζ90−ζ106ζ26−ζ30+ζ58−ζ110−ζ26+ζ30−ζ58+ζ110ζ10−ζ46+ζ74−ζ94−ζ10+ζ46−ζ74+ζ94000000000000

Here ζ is a primitive root of unity of order 112 (ζ112 = 1).