Finite Group Databasebeta

← Group #97331

Character table — Group #97331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444224444888888882244444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-1111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ811111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i1-1-1-11-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i-11-1-1-11-11-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiii1-1-1-11-11-11-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiii-11-1-1-11-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-111-1-1-1-1-1-11-1-11iiii−i−i−i−i1-111-111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-111-1-1-1-1-1-11-1-11iiii−i−i−i−i-11111-1-111-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-1-1-111-1-1-1-1-1-11-1-11−i−i−i−iiiii1-111-111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-111-1-1-1-1-1-11-1-11−i−i−i−iiiii-11111-1-111-1ii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-2-22-200200-20000000000002200-2-2000000000000
χ182222222222222-2-2-2-2-22-200200-2000000000000-2-20022000000000000
χ19222222222222-22-2-2-2-2-2200-200200000000220000-2-200000000000000
χ20222222222222-22-2-2-2-2-2200-200200000000-2-200002200000000000000
χ21222222222222-2-22222-2-222-2-2-2-200000000002-2000000000000000000
χ22222222222222-2-22222-2-2-2-2-222-20000000000-22000000000000000000
χ2322222222-2-2-2-22222-2-22222-2-2-2-20000000000-22000000000000000000
χ2422222222-2-2-2-22222-2-222-2-2-222-200000000002-2000000000000000000
χ2522222222-2-2-2-22-2-2-2222-200-2002000000002-20000-2200000000000000
χ2622222222-2-2-2-22-2-2-2222-200-200200000000-2200002-200000000000000
χ2722222222-2-2-2-2-22-2-222-2200200-20000000000002-200-22000000000000
χ2822222222-2-2-2-2-22-2-222-2200200-2000000000000-22002-2000000000000
χ29444-44-4-4-400000400000-400000022-2-222-2-20000000000000000000000
χ30444-44-4-4-400000400000-4000000-2-222-2-2220000000000000000000000
χ31444-44-4-4-400000-40000040000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ32444-44-4-4-400000-4000004000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ3344-44-44-4-444-4-40000000000000000000000000000000000002-22-20000
χ3444-44-44-4-444-4-4000000000000000000000000000000000000-22-220000
χ3544-44-44-4-4-4-4440000000000000000000000000000000000002i−2i−2i2i0000
χ3644-44-44-4-4-4-444000000000000000000000000000000000000−2i2i2i−2i0000
χ3744-4-4-4-4440000004-400000004-40000000000000000000000000000000
χ3844-4-4-4-4440000004-40000000-440000000000000000000000000000000
χ3944-4-4-4-444000000-4400004-40000000000000000000000000000000000
χ4044-4-4-4-444000000-440000-440000000000000000000000000000000000
χ414-444-4-44-4000000004i−4i000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ424-444-4-44-4000000004i−4i00000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ434-444-4-44-400000000−4i4i000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ444-444-4-44-400000000−4i4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ454-44-4-44-444-44-400000000000000000000000000000000000000002i−2i2i−2i
χ464-44-4-44-444-44-40000000000000000000000000000000000000000−2i2i−2i2i
χ474-44-4-44-44-44-4400000000000000000000000000000000000000002-2-22
χ484-44-4-44-44-44-440000000000000000000000000000000000000000-222-2
χ494-4-444-4-440000400000-400000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ504-4-444-4-440000400000-40000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ514-4-444-4-440000-400000400000002-22-2-22-220000000000000000000000
χ524-4-444-4-440000-40000040000000-22-222-22-20000000000000000000000
χ534-4-4-4444-44-4-44000000000000002-2-22-222-20000000000000000000000
χ544-4-4-4444-44-4-4400000000000000-222-22-2-220000000000000000000000
χ554-4-4-4444-4-444-4000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ564-4-4-4444-4-444-400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000

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