Finite Group Databasebeta

← Group #98113

Character table — Group #98113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size111111114444444488816161616161616161616161616161616161616161616161616161616
order12222222224444444442444444444444444888888888888
χ111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-11-1-1-11-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111-1-11-1-1-11-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111-1-111-11-1-1-11-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111-1-111-11-1-1-11-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1
χ81111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-11111-111-1-11-11-11-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-111-1-11-11-11-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1111-11ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11-1111-11−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1111-11111-1-11-1-1-11ii−i−i−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-1-1-1-1-1111-11111-1-11-1-1-11−i−iiiii−i−iii−i−i−i−iii
χ1511111111-1-1-1-1-1-1-1-1111-11-1-1111-1-111-1ii−i−iii−i−i−i−iii−i−iii
χ1611111111-1-1-1-1-1-1-1-1111-11-1-1111-1-111-1−i−iii−i−iiiii−i−iii−i−i
χ1722222222222-2-2-22-22-2-22-2002000-20000000000000000000
χ1822222222222-2-2-22-22-2-2-2200-200020000000000000000000
χ192222222222-22-2-2-22-22-2002-202000-2000000000000000000
χ202222222222-22-2-2-22-22-200-220-20002000000000000000000
χ212222222222-2-222-2-2-2-220000002-200-220000000000000000
χ222222222222-2-222-2-2-2-22000000-22002-20000000000000000
χ2322222222-2-222-2-222-2-220000002200-2-20000000000000000
χ2422222222-2-222-2-222-2-22000000-2-200220000000000000000
χ2522222222-2-22-2222-2-22-2002-20-20002000000000000000000
χ2622222222-2-22-2222-2-22-200-2202000-2000000000000000000
χ2722222222-2-2-2222-222-2-22200-2000-20000000000000000000
χ2822222222-2-2-2222-222-2-2-2-200200020000000000000000000
χ29444-4-44-4-40004000-40000000000000002-22-2000000000000
χ30444-4-44-4-40004000-4000000000000000-22-22000000000000
χ31444-4-44-4-4000-400040000000000000002i−2i−2i2i000000000000
χ32444-4-44-4-4000-40004000000000000000−2i2i2i−2i000000000000
χ3344-44-4-44-44-400000000000000000000000002-22-200000000
χ3444-44-4-44-44-40000000000000000000000000-22-2200000000
χ3544-44-4-44-4-4400000000000000000000000002i−2i−2i2i00000000
χ3644-44-4-44-4-440000000000000000000000000−2i2i2i−2i00000000
χ3744-4-44-4-4400004i−4i000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3844-4-44-4-4400004i−4i00000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3944-4-44-4-440000−4i4i000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ4044-4-44-4-440000−4i4i00000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ414-4-4-4444-4004000-40000000000000000000000002i−2i2i−2i0000
χ424-4-4-4444-4004000-4000000000000000000000000−2i2i−2i2i0000
χ434-4-4-4444-400-400040000000000000000000000002-2-220000
χ444-4-4-4444-400-40004000000000000000000000000-222-20000
χ458-8888-8-8-8000000000000000000000000000000000000000
χ468-88-8-8-888000000000000000000000000000000000000000
χ478-8-88-88-88000000000000000000000000000000000000000

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