Finite Group Databasebeta

← Group #459713

Character table — Group #459713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222222244448888888888161616161616161616161616161616161616161616161616
order12442222222444444488884444888888224444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-11-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111111111111-11-11-1-111-1-1-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1111111-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-11-111111-1-111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-11-11-1-1-111-1-111111111-1-1-1-1-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-11-1111-1-11111-1-111-1-111-1-1-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111111-11-11111-1-1-1-1-1-111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-1111111-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ172222222-2-2-2-22-22-22-2-200002i2i−2i−2i0000000000002i−2i00002-20000000000
χ182222222-2-2-2-22-22-22-2-200002i2i−2i−2i000000000000−2i2i0000-220000000000
χ192222222-2-2-2-22-22-22-2-20000−2i−2i2i2i0000000000002i−2i0000-220000000000
χ202222222-2-2-2-22-22-22-2-20000−2i−2i2i2i000000000000−2i2i00002-20000000000
χ2122222-2-22-2-2222-22-2-2-200000000002i2i−2i−2i000000000000002-20000002i−2i
χ2222222-2-22-2-2222-22-2-2-200000000002i2i−2i−2i00000000000000-22000000−2i2i
χ2322222-2-22-2-2222-22-2-2-20000000000−2i−2i2i2i000000000000002-2000000−2i2i
χ2422222-2-22-2-2222-22-2-2-20000000000−2i−2i2i2i00000000000000-220000002i−2i
χ252222-22-2-2-222-22-2-222-222220000-2-2000000002-200000000002-2000000
χ262222-22-2-2-222-22-2-222-222220000-2-200000000-220000000000-22000000
χ272222-22-2-2-222-22-2-222-2-2-2-2-2000022000000002-20000000000-22000000
χ282222-22-2-2-222-22-2-222-2-2-2-2-200002200000000-2200000000002-2000000
χ2922-2-2222-2-2-2-2-22-22-22200000000002i−2i2i−2i00000000002i−2i000000002-200
χ3022-2-2222-2-2-2-2-22-22-22200000000002i−2i2i−2i0000000000−2i2i00000000-2200
χ3122-2-2222-2-2-2-2-22-22-2220000000000−2i2i−2i2i00000000002i−2i00000000-2200
χ3222-2-2222-2-2-2-2-22-22-2220000000000−2i2i−2i2i0000000000−2i2i000000002-200
χ3322-2-22-2-22-2-22-2-22-222200002-22-2000000020-2000000000000002-20000
χ3422-2-22-2-22-2-22-2-22-222200002-22-20000000-20200000000000000-220000
χ3522-2-22-2-22-2-22-2-22-22220000-22-22000000020-200000000000000-220000
χ3622-2-22-2-22-2-22-2-22-22220000-22-220000000-202000000000000002-20000
χ3722-2-22-2-2-222-2-22222-2-22i2i−2i−2i2i−2i−2i2i2i−2i2-2-22000000000000000000000000
χ3822-2-22-2-2-222-2-22222-2-22i2i−2i−2i−2i2i2i−2i2i−2i-222-2000000000000000000000000
χ3922-2-22-2-2-222-2-22222-2-2−2i−2i2i2i2i−2i−2i2i−2i2i-222-2000000000000000000000000
χ4022-2-22-2-2-222-2-22222-2-2−2i−2i2i2i−2i2i2i−2i−2i2i2-2-22000000000000000000000000
χ4122-2-2-2-222-22-222-2-22-222i2i−2i−2i0000−2i2i000020-2000002i−2i00000000000000
χ4222-2-2-2-222-22-222-2-22-222i2i−2i−2i0000−2i2i0000-20200000−2i2i00000000000000
χ4322-2-2-2-222-22-222-2-22-22−2i−2i2i2i00002i−2i000020-200000−2i2i00000000000000
χ4422-2-2-2-222-22-222-2-22-22−2i−2i2i2i00002i−2i0000-202000002i−2i00000000000000
χ4544444-4-4-444-44-4-4-4-44400000000000000000000000000000000000000
χ464444-44-444-4-4-4-4-444-4400000000000000000000000000000000000000
χ474444-4-444-44-4-4-444-44-400000000000000000000000000000000000000
χ484444-4-44-44-44-444-4-4-4400000000000000000000000000000000000000
χ4944-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000
χ5044-4-4-44-444-4-4444-4-44-400000000000000000000000000000000000000
χ5144-4-4-44-4-4-4444-444-4-4400000000000000000000000000000000000000
χ5244-4-4-4-44-44-444-4-4444-400000000000000000000000000000000000000
χ538-88i−8i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000
χ548-88i−8i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000
χ558-8−8i8i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000
χ568-8−8i8i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000

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