Finite Group Databasebeta

← Group #97337

Character table — Group #97337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888882244444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-11-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-11-1-111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ8111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i1-1-11-1-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-1111111iiii−i−i−i−i-11-1-11-1-11-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii1-1-11-1-11-11-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-1111111−i−i−i−iiiii-11-1-11-1-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-11-1-11-1-1iiii−i−i−i−i1-11-1111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-11-1-11-1-1iiii−i−i−i−i-1111-11-111-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-11-1-11-1-1−i−i−i−iiiii1-11-1111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-11-1-11-1-1−i−i−i−iiiii-1111-11-111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-222-2-2-222-2-2-20000000000-20020000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2220000000000200-20000000000000000
χ19222222222222-2-22-2-2-22-2-20020000000000220000-2-200000000000000
χ20222222222222-2-22-2-2-22-2-20020000000000-2-200002200000000000000
χ21222222222222-2-2-22-2-2-22200-2000000000000022000-2-2000000000000
χ22222222222222-2-2-22-2-2-22200-20000000000000-2-200022000000000000
χ2322222222-2-2-2-22222-2-222-222-2-2-20000000000200-20000000000000000
χ2422222222-2-2-2-22222-2-222-2-2-2-2220000000000-20020000000000000000
χ2522222222-2-2-2-2-2-22-2222-2200-200000000000002-2000-22000000000000
χ2622222222-2-2-2-2-2-22-2222-2200-20000000000000-220002-2000000000000
χ2722222222-2-2-2-2-2-2-2222-22-200200000000002-20000-2200000000000000
χ2822222222-2-2-2-2-2-2-2222-22-20020000000000-2200002-200000000000000
χ29444-4-44-4-444-4-40000000000000022-2-222-2-20000000000000000000000
χ30444-4-44-4-444-4-400000000000000-2-222-2-2220000000000000000000000
χ31444-4-44-4-4-4-444000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ32444-4-44-4-4-4-44400000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ3344-444-4-4-40000004000-400000002-22-22-22-20000000000000000000000
χ3444-444-4-4-40000004000-40000000-22-22-22-220000000000000000000000
χ3544-444-4-4-4000000-4000400000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ3644-444-4-4-4000000-400040000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ3744-4-4-4-44400000004000-40000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ3844-4-4-4-44400000004000-4000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ3944-4-4-4-4440000000-400040000002-2-222-2-220000000000000000000000
χ4044-4-4-4-4440000000-40004000000-222-2-222-20000000000000000000000
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
χ454-44-44-4-4400004-400000000004i−4i000000000000000000000000000000
χ464-44-44-4-4400004-40000000000−4i4i000000000000000000000000000000
χ474-44-44-4-440000-4400000004i−4i000000000000000000000000000000000
χ484-44-44-4-440000-440000000−4i4i000000000000000000000000000000000
χ494-4-44-44-444-44-400000000000000000000000000000000000000002i−2i2i−2i
χ504-4-44-44-444-44-40000000000000000000000000000000000000000−2i2i−2i2i
χ514-4-44-44-44-44-4400000000000000000000000000000000000000002-2-22
χ524-4-44-44-44-44-440000000000000000000000000000000000000000-222-2
χ534-4-4-4444-44-4-440000000000000000000000000000000000002-22-20000
χ544-4-4-4444-44-4-44000000000000000000000000000000000000-22-220000
χ554-4-4-4444-4-444-40000000000000000000000000000000000002i−2i−2i2i0000
χ564-4-4-4444-4-444-4000000000000000000000000000000000000−2i2i2i−2i0000

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