Finite Group Databasebeta

← Group #6739

Character table — Group #6739

Order 240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24
size1122445568810101010101010101212303030
order12365104421530881212242424241010488
χ1111111111111111111111111
χ211111111111-1-111-1-1-1-1111-1-1
χ311111111-11111111111-1-1-1-1-1
χ411111111-111-1-111-1-1-1-1-1-1-111
χ5111111-1-1111i−i-1-1ii−i−i11-1i−i
χ6111111-1-1111−ii-1-1−i−iii11-1−ii
χ7111111-1-1-111i−i-1-1ii−i−i-1-11−ii
χ8111111-1-1-111−ii-1-1−i−iii-1-11i−i
χ922-1-122220-1-122-1-1-1-1-1-100000
χ1022-1-122220-1-1-2-2-1-1111100000
χ1122-1-122-2-20-1-12i−2i11−i−iii00000
χ1222-1-122-2-20-1-1−2i2i11ii−i−i00000
χ132-22-22-22i−2i02-2002i−2i000000000
χ142-22-22-2−2i2i02-200−2i2i000000000
χ152-2-112-22i−2i0-1100−iiζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ10900000
χ162-2-112-22i−2i0-1100−ii−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ10900000
χ172-2-112-2−2i2i0-1100i−iζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ11900000
χ182-2-112-2−2i2i0-1100i−i−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ11900000
χ194444-1-1004-1-100000000-1-1000
χ204444-1-100-4-1-10000000011000
χ214-44-4-11000-1100000000−55000
χ224-44-4-11000-11000000005−5000
χ2388-4-4-2-2000110000000000000
χ248-8-44-220001-10000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.