Finite Group Databasebeta

← Group #97474

Character table — Group #97474

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111114444444444444488888888888816161616161616161616161616161616161616161616
order12222222224444444444442222444444442444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-22222-2-2-2-222-2-2000000000002-200000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-22200000000000-2200000000000000000
χ192222222222-2-2-2-2-2-2-2-2222222-2-200000000000-2200000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-222000000000002-200000000000000000
χ2122222222-2-222-2-222-2-222-2-20000000022-2-202-20000000000000000000
χ2222222222-2-222-2-222-2-222-2-200000000-2-2220-220000000000000000000
χ2322222222-2-222-2-2-2-222-2-2220000000022-2-20-220000000000000000000
χ2422222222-2-222-2-2-2-222-2-22200000000-2-22202-20000000000000000000
χ2522222222-2-2-2-22222-2-2-2-222000022-2-2000020000-20000000000000000
χ2622222222-2-2-2-22222-2-2-2-2220000-2-2220000-2000020000000000000000
χ2722222222-2-2-2-222-2-22222-2-2000022-2-20000-2000020000000000000000
χ2822222222-2-2-2-222-2-22222-2-20000-2-222000020000-20000000000000000
χ29444-4-4-4-4400004-4000000000000004i−4i00000000000000000000000000
χ30444-4-4-4-4400004-400000000000000−4i4i00000000000000000000000000
χ31444-4-4-4-440000-440000000000004i−4i0000000000000000000000000000
χ32444-4-4-4-440000-44000000000000−4i4i0000000000000000000000000000
χ3344-444-4-4-40000000000004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3444-444-4-4-40000000000004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3544-444-4-4-4000000000000−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3644-444-4-4-4000000000000−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3744-4-4-444-4000000004i−4i00000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ3844-4-4-444-4000000004i−4i0000000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ3944-4-4-444-400000000−4i4i00000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ4044-4-4-444-400000000−4i4i0000000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ414-444-44-4-400000000004i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ424-444-44-4-400000000004i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ434-444-44-4-40000000000−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ444-444-44-4-40000000000−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ454-44-44-44-40000004i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ464-44-44-44-40000004i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ474-44-44-44-4000000−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ484-44-44-44-4000000−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ494-4-44-4-4444-4000000000000004-4000000000000000000000000000000
χ504-4-44-4-4444-400000000000000-44000000000000000000000000000000
χ514-4-44-4-444-440000000000004-400000000000000000000000000000000
χ524-4-44-4-444-44000000000000-4400000000000000000000000000000000
χ534-4-4-444-44004-4000000000000000000004-40000000000000000000000
χ544-4-4-444-44004-400000000000000000000-440000000000000000000000
χ554-4-4-444-4400-440000000000000000004-4000000000000000000000000
χ564-4-4-444-4400-44000000000000000000-44000000000000000000000000

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