Finite Group Databasebeta

← Group #471078

Character table — Group #471078

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222222244448888888888161616161616161616161616161616161616161616161616
order12442222222444444488884444888888244444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111
χ9111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1
χ1722222-222-2-2-2-222-2-22-200002i2i−2i−2i0000000000002-2002i−2i000000000000
χ1822222-222-2-2-2-222-2-22-200002i2i−2i−2i000000000000-2200−2i2i000000000000
χ1922222-222-2-2-2-222-2-22-20000−2i−2i2i2i0000000000002-200−2i2i000000000000
χ2022222-222-2-2-2-222-2-22-20000−2i−2i2i2i000000000000-22002i−2i000000000000
χ2122222-2-2-22-2222-2-2-2-22000000002i2i−2i−2i00002i−2i00002-200000000000000
χ2222222-2-2-22-2222-2-2-2-22000000002i2i−2i−2i0000−2i2i0000-2200000000000000
χ2322222-2-2-22-2222-2-2-2-2200000000−2i−2i2i2i00002i−2i0000-2200000000000000
χ2422222-2-2-22-2222-2-2-2-2200000000−2i−2i2i2i0000−2i2i00002-200000000000000
χ252222-2-22-222-22-2-22-22-2222200000000-2-2000000000000002i−2i2i−2i000000
χ262222-2-22-222-22-2-22-22-2222200000000-2-200000000000000−2i2i−2i2i000000
χ272222-2-22-222-22-2-22-22-2-2-2-2-20000000022000000000000002i−2i−2i2i000000
χ282222-2-22-222-22-2-22-22-2-2-2-2-2000000002200000000000000−2i2i2i−2i000000
χ2922-2-22222222-2-2-2-2-2-2-200002-22-20000000000000000000000002i−2i2i−2i00
χ3022-2-22222222-2-2-2-2-2-2-200002-22-2000000000000000000000000−2i2i−2i2i00
χ3122-2-22222222-2-2-2-2-2-2-20000-22-220000000000000000000000002i−2i−2i2i00
χ3222-2-22222222-2-2-2-2-2-2-20000-22-22000000000000000000000000−2i2i2i−2i00
χ3322-2-222-2-2-22-22-22-2-222000000002i−2i2i−2i002-2002i−2i000000000000000000
χ3422-2-222-2-2-22-22-22-2-222000000002i−2i2i−2i00-2200−2i2i000000000000000000
χ3522-2-222-2-2-22-22-22-2-22200000000−2i2i−2i2i002-200−2i2i000000000000000000
χ3622-2-222-2-2-22-22-22-2-22200000000−2i2i−2i2i00-22002i−2i000000000000000000
χ3722-2-22-222-2-2-22-2-222-222i2i−2i−2i2i−2i−2i2i2-2-222i−2i000000000000000000000000
χ3822-2-22-222-2-2-22-2-222-222i2i−2i−2i−2i2i2i−2i-222-22i−2i000000000000000000000000
χ3922-2-22-222-2-2-22-2-222-22−2i−2i2i2i2i−2i−2i2i-222-2−2i2i000000000000000000000000
χ4022-2-22-222-2-2-22-2-222-22−2i−2i2i2i−2i2i2i−2i2-2-22−2i2i000000000000000000000000
χ4122-2-2-222-2-2-222222-2-2-22i2i−2i−2i00000000−2i2i0000000000002-2000000002i−2i
χ4222-2-2-222-2-2-222222-2-2-22i2i−2i−2i00000000−2i2i000000000000-2200000000−2i2i
χ4322-2-2-222-2-2-222222-2-2-2−2i−2i2i2i000000002i−2i0000000000002-200000000−2i2i
χ4422-2-2-222-2-2-222222-2-2-2−2i−2i2i2i000000002i−2i000000000000-22000000002i−2i
χ45444444-4-4-44-4-44-444-4-400000000000000000000000000000000000000
χ464444-444-4-4-44-4-4-4-444400000000000000000000000000000000000000
χ474444-44-444-4-44-44-44-4-400000000000000000000000000000000000000
χ484444-4-4-44-444-4-444-4-4400000000000000000000000000000000000000
χ4944-4-44-4-4-44-44-4-44444-400000000000000000000000000000000000000
χ5044-4-4-44-444-4-4-44-44-44400000000000000000000000000000000000000
χ5144-4-4-4-44-444-4-444-44-4400000000000000000000000000000000000000
χ5244-4-4-4-4-44-44444-4-444-400000000000000000000000000000000000000
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.