Finite Group Databasebeta

← Group #97446

Character table — Group #97446

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111114444444444444488888888888816161616161616161616161616161616161616161616
order12222222222222444444442244444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-111-111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-111111111
χ91111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111-111-1ii−i−i−i−iiiii−i−i−i−iii
χ121111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111-111-1−i−iiiii−i−i−i−iiiii−i−i
χ131111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ141111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11ii−i−iii−i−i−i−iii−i−iii
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11−i−iii−i−iiiii−i−iii−i−i
χ1722222222222222-2-2-2-2-2-2-2-20000000022-2-20002-200000000000000000
χ1822222222222222-2-2-2-2-2-2-2-200000000-2-222000-2200000000000000000
χ192222222222-2-2-2-2-2-2-2-222220000000022-2-2000-2200000000000000000
χ202222222222-2-2-2-2-2-2-2-2222200000000-2-2220002-200000000000000000
χ2122222222-2-22-22-222-2-222-2-2002200-2-200002-200000000000000000000
χ2222222222-2-22-22-222-2-222-2-200-2-200220000-2200000000000000000000
χ2322222222-2-22-22-2-2-222-2-2222200-2-200000000200-20000000000000000
χ2422222222-2-22-22-2-2-222-2-222-2-2002200000000-20020000000000000000
χ2522222222-2-2-22-2222-2-2-2-222002200-2-20000-2200000000000000000000
χ2622222222-2-2-22-2222-2-2-2-22200-2-2002200002-200000000000000000000
χ2722222222-2-2-22-22-2-22222-2-22200-2-200000000-20020000000000000000
χ2822222222-2-2-22-22-2-22222-2-2-2-2002200000000200-20000000000000000
χ29444-44-4-4-40040-400000000000000000000000000000002-22-200000000
χ30444-44-4-4-40040-40000000000000000000000000000000-22-2200000000
χ31444-44-4-4-400-40400000000000000000000000000000002i−2i−2i2i00000000
χ32444-44-4-4-400-4040000000000000000000000000000000−2i2i2i−2i00000000
χ3344-44-4-4-440000000000004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3444-44-4-4-440000000000004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3544-44-4-4-44000000000000−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3644-44-4-4-44000000000000−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3744-4-4-444-40000004-40000000000004i−4i00000000000000000000000000
χ3844-4-4-444-40000004-4000000000000−4i4i00000000000000000000000000
χ3944-4-4-444-4000000-44000000004i−4i000000000000000000000000000000
χ4044-4-4-444-4000000-4400000000−4i4i000000000000000000000000000000
χ414-444-4-44-44-400000000000000000000004i−4i0000000000000000000000
χ424-444-4-44-44-40000000000000000000000−4i4i0000000000000000000000
χ434-444-4-44-4-44000000000000000000004i−4i000000000000000000000000
χ444-444-4-44-4-4400000000000000000000−4i4i000000000000000000000000
χ454-44-4-44-4400040-4000000000000000000000000002i−2i2i−2i000000000000
χ464-44-4-44-4400040-400000000000000000000000000−2i2i−2i2i000000000000
χ474-44-4-44-44000-404000000000000000000000000002-2-22000000000000
χ484-44-4-44-44000-40400000000000000000000000000-222-2000000000000
χ494-4-4444-4-400000000004i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ504-4-4444-4-400000000004i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ514-4-4444-4-40000000000−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ524-4-4444-4-40000000000−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ534-4-4-44-444000000004-4000000004-40000000000000000000000000000
χ544-4-4-44-444000000004-400000000-440000000000000000000000000000
χ554-4-4-44-44400000000-4400004-400000000000000000000000000000000
χ564-4-4-44-44400000000-440000-4400000000000000000000000000000000

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