Finite Group Databasebeta

← Group #98330

Character table — Group #98330

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444444244444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1111-1-111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111-1-111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-11-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1
χ911111111-1-111-1-111-1-1-1-111111-1-111-11-111-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-111-1-111-1-1-1-111111-1-111-11-111-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-111-1-111-1-1-1-1111-1-1-1-1-1-1-111-1-1111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-111-1-111-1-1-1-1111-1-1-1-1-1-1-111-1-1111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-111-1-111-1-1-1-1-1-11-1-111-1-11-1111-1-11ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-111-1-111-1-1-1-1-1-11-1-111-1-11-1111-1-11−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-2-22-222-2002200-2-20000000000000000000000
χ182222222222222-2-2-2-2-22-2-2-2-200-2-200220000000000000000000000
χ192222222222-2-2-22-2-2-2-2-220020000000002-22-200000000000000000
χ202222222222-2-2-22-2-2-2-2-22002000000000-22-2200000000000000000
χ212222222222-2-2-2-22222-2-200-22200-2-200-2000020000000000000000
χ222222222222-2-2-2-22222-2-200-2-2-200220020000-20000000000000000
χ2322222222-2-222-22-2-222-2222-200-2-2002-20000000000000000000000
χ2422222222-2-222-22-2-222-22-2-2-2002200-220000000000000000000000
χ2522222222-2-2-2-22222-2-22200-22200-2-20020000-20000000000000000
χ2622222222-2-2-2-22222-2-22200-2-2-2002200-2000020000000000000000
χ2722222222-2-2-2-22-2-2-2222-20020000000002-2-2200000000000000000
χ2822222222-2-2-2-22-2-2-2222-2002000000000-222-200000000000000000
χ2922-2-222-2-22-22-2-200000202i−2i0002i−2i000000000000002−22−20000i2−i2i2−i2
χ3022-2-222-2-22-22-2-200000202i−2i0002i−2i00000000000000−22−220000−i2i2−i2i2
χ3122-2-222-2-22-22-2-20000020−2i2i000−2i2i000000000000002−22−20000−i2i2−i2i2
χ3222-2-222-2-22-22-2-20000020−2i2i000−2i2i00000000000000−22−220000i2−i2i2−i2
χ3322-2-222-2-2-222-2200000-202i−2i000−2i2i00000000000000i2−i2−i2i20000−222−2
χ3422-2-222-2-2-222-2200000-202i−2i000−2i2i00000000000000−i2i2i2−i200002−2−22
χ3522-2-222-2-2-222-2200000-20−2i2i0002i−2i00000000000000i2−i2−i2i200002−2−22
χ3622-2-222-2-2-222-2200000-20−2i2i0002i−2i00000000000000−i2i2i2−i20000−222−2
χ3744-44-4-44-400000400000-4000000000000000002-22-2000000000000
χ3844-44-4-44-400000400000-400000000000000000-22-22000000000000
χ3944-44-4-44-400000-4000004000000000000000002i−2i−2i2i000000000000
χ4044-44-4-44-400000-400000400000000000000000−2i2i2i−2i000000000000
χ4144-4-444-4-44-4-44400000-40000000000000000000000000000000000
χ4244-4-444-4-4-44-44-40000040000000000000000000000000000000000
χ434-44-44-44-4000000004i−4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ444-44-44-44-4000000004i−4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ454-44-44-44-400000000−4i4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ464-44-44-44-400000000−4i4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ474-4-4-4-44440000004-4000000000004-4000000000000000000000000
χ484-4-4-4-44440000004-400000000000-44000000000000000000000000
χ494-4-4-4-4444000000-4400000004-40000000000000000000000000000
χ504-4-4-4-4444000000-440000000-440000000000000000000000000000
χ51888-8-8-8-88000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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