Finite Group Databasebeta

← Group #168

Character table — Group #168

Order 40.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16
size1111222222225555
order1244551010202020208888
χ11111111111111111
χ2111111111111-1-1-1-1
χ311-1-11111-1-1-1-1ii−i−i
χ411-1-11111-1-1-1-1−i−iii
χ51-1i−i11-1-1ii−i−i−ζ13−ζ21−ζ29−ζ37ζ13+ζ21+ζ29+ζ37−ζ7−ζ23−ζ31−ζ39ζ7+ζ23+ζ31+ζ39
χ61-1i−i11-1-1ii−i−iζ13+ζ21+ζ29+ζ37−ζ13−ζ21−ζ29−ζ37ζ7+ζ23+ζ31+ζ39−ζ7−ζ23−ζ31−ζ39
χ71-1−ii11-1-1−i−iii−ζ7−ζ23−ζ31−ζ39ζ7+ζ23+ζ31+ζ39−ζ13−ζ21−ζ29−ζ37ζ13+ζ21+ζ29+ζ37
χ81-1−ii11-1-1−i−iiiζ7+ζ23+ζ31+ζ39−ζ7−ζ23−ζ31−ζ39ζ13+ζ21+ζ29+ζ37−ζ13−ζ21−ζ29−ζ37
χ92222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000
χ102222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000
χ1122-2-2−1+52−1−52−1+52−1−521−521+521−521+520000
χ1222-2-2−1−52−1+52−1−52−1+521+521−521+521−520000
χ132-22i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000
χ142-22i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000
χ152-2−2i2i−1+52−1−521−521+52ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000
χ162-2−2i2i−1−52−1+521+521−52ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.