Finite Group Databasebeta

← Group #150802

Character table — Group #150802

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size1111224444444488888881616161616161616161616161616323232323232
order1244242488888822444482244881616161616161616888888
χ111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-11-11-1-1-1111111-1iiii−i−i−i−i-1-1ii−i−i
χ61111111111-1-1-1-11-11-1-1-1111111-1−i−i−i−iiiii-1-1−i−iii
χ71111111111-1-1-1-11-11-1-1-11-1-1-1-11-1iiii−i−i−i−i11−i−iii
χ81111111111-1-1-1-11-11-1-1-11-1-1-1-11-1−i−i−i−iiiii11ii−i−i
χ911111111-1-11111-11-1-1-11-11-11-11-111-1-111-1-11-11-11-1
χ1011111111-1-11111-11-1-1-11-11-11-11-1-1-111-1-1111-1-11-11
χ1111111111-1-11111-11-1-1-11-1-11-111-111-1-111-1-1-11-11-11
χ1211111111-1-11111-11-1-1-11-1-11-111-1-1-111-1-111-111-11-1
χ1311111111-1-1-1-1-1-1-1-1-111-1-11-11-111ii−i−i−i−iii-11i−i−ii
χ1411111111-1-1-1-1-1-1-1-1-111-1-11-11-111−i−iiiii−i−i-11−iii−i
χ1511111111-1-1-1-1-1-1-1-1-111-1-1-11-1111ii−i−i−i−iii1-1−iii−i
χ1611111111-1-1-1-1-1-1-1-1-111-1-1-11-1111−i−iiiii−i−i1-1i−i−ii
χ1722222222222222-2-2-222-220000-2-200000000000000
χ182222222222-2-2-2-2-22-2-2-2220000-2200000000000000
χ1922222222-2-222222-22-2-2-2-20000-2200000000000000
χ2022222222-2-2-2-2-2-2222222-20000-2-200000000000000
χ2122-2-22-2-2200000022-22-2-20000000i2−i2i2−i2i2−i2i2−i2000000
χ2222-2-22-2-2200000022-22-2-20000000−i2i2−i2i2−i2i2−i2i2000000
χ2322-2-22-2-220000002-2-2-22200000002−22−2−22−22000000
χ2422-2-22-2-220000002-2-2-2220000000−22−222−22−2000000
χ2522-2-22-2-22000000-222-22-20000000i2−i2−i2i2i2−i2−i2i2000000
χ2622-2-22-2-22000000-222-22-20000000−i2i2i2−i2−i2i2i2−i2000000
χ2722-2-22-2-22000000-2-222-2200000002−2−22−222−2000000
χ2822-2-22-2-22000000-2-222-220000000−222−22−2−22000000
χ29444444-4-4440000000000-400000000000000000000
χ30444444-4-4-4-40000000000400000000000000000000
χ3144-4-44-44-4004i4i−4i−4i000000000000000000000000000
χ3244-4-44-44-400−4i−4i4i4i000000000000000000000000000
χ3344-4-4-44004-40000000000022-2-20000000000000000
χ3444-4-4-44004-400000000000-2-2220000000000000000
χ3544-4-4-4400-44000000000002-2-220000000000000000
χ3644-4-4-4400-4400000000000-222-20000000000000000
χ378888-8-800000000000000000000000000000000000
χ388-88i−8i0000004ζ−4ζ4ζ3−4ζ3000000000000000000000000000
χ398-88i−8i000000−4ζ4ζ−4ζ34ζ3000000000000000000000000000
χ408-8−8i8i0000004ζ3−4ζ34ζ−4ζ000000000000000000000000000
χ418-8−8i8i000000−4ζ34ζ3−4ζ4ζ000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.