Finite Group Databasebeta

← Group #152248

Character table — Group #152248

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111224444444444888888888888881616161616163232323232323232
order12442424888888882244444444888844888844444444
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111-1-1-1-11111111111-1-1-1-1-1-1ii−i−iii−i−i
χ61111111111111111-1-1-1-11111111111-1-1-1-1-1-1−i−iii−i−iii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i
χ911111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11-11-11-11-1
χ1011111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-11-11-11-11
χ1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11-11-1-11-11
χ1211111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-11-111-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111i−i−iii−i−ii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111−iii−i−iii−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111i−i−ii−iii−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111−iii−ii−i−ii
χ17222222222222-2-2-2-22-22-2-2-20000000000002-200000000
χ18222222222222-2-2-2-2-22-22-2-2000000000000-2200000000
χ1922222222-2-2-2-222222-22-2-2-2000000000000-2200000000
χ2022222222-2-2-2-22222-22-22-2-20000000000002-200000000
χ2122-2-22-2-220000000022-2-22-2000022-2-22-2000000000000
χ2222-2-22-2-220000000022-2-22-20000-2-222-22000000000000
χ2322-2-22-2-22000000002-2-22-222i2i−2i−2i0000002i−2i0000000000
χ2422-2-22-2-22000000002-2-22-22−2i−2i2i2i000000−2i2i0000000000
χ2522-2-22-2-2200000000-222-2-222i2i−2i−2i000000−2i2i0000000000
χ2622-2-22-2-2200000000-222-2-22−2i−2i2i2i0000002i−2i0000000000
χ2722-2-22-2-2200000000-2-2222-2000022-2-2-22000000000000
χ2822-2-22-2-2200000000-2-2222-20000-2-2222-2000000000000
χ29444444-4-4000044-4-40000000000000000000000000000
χ30444444-4-40000-4-4440000000000000000000000000000
χ314444-4-4000000004i−4i0000002-22-22i−2i2i−2i00000000000000
χ324444-4-4000000004i−4i000000-22-22−2i2i−2i2i00000000000000
χ334444-4-400000000−4i4i0000002-22-2−2i2i−2i2i00000000000000
χ344444-4-400000000−4i4i000000-22-222i−2i2i−2i00000000000000
χ3544-4-44-44-44i4i−4i−4i00000000000000000000000000000000
χ3644-4-44-44-4−4i−4i4i4i00000000000000000000000000000000
χ3744-4-4-440000004-4000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ3844-4-4-440000004-400000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ3944-4-4-44000000-44000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ4044-4-4-44000000-4400000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ418-88i−8i00004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000
χ428-88i−8i0000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000
χ438-8−8i8i00004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000
χ448-8−8i8i0000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000

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