Finite Group Databasebeta

← Group #471534

Character table — Group #471534

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222222244448888888888161616161616161616161616161616161616161616161616
order12442222222444444488884444888888222444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111-1-11-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ51111111111111111111111-1-1-1-111-1-1-1-11-111-11-1-111-1-1-1-11111-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11-1-11-1-111-1-11111-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-111-111-1-1-1-111-1-111-1-111-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-11-1-11-11111-1-111-1-111-1-1-1-111
χ9111111111111111111-1-1-1-11111-1-1-1-1-1-11-111-11-1-1111111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1111111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-1111111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-11-1-11-1111111-1-111-1-1-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111111111-1-1-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1111-1-111-1-1-1-111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1111111
χ1722222-2-222-2-2-2-222-2-22222222-2-2-2-222-2-2000000000000000000000000
χ1822222-2-222-2-2-2-222-2-222222-2-222-2-2-2-222000000000000000000000000
χ1922222-2-222-2-2-2-222-2-22-2-2-2-222-2-222-2-222000000000000000000000000
χ2022222-2-222-2-2-2-222-2-22-2-2-2-2-2-2222222-2-2000000000000000000000000
χ2122-2-22222222-2-2-2-2-2-2-22i2i−2i−2i00002i−2i0000000000002-20000002i−2i000000
χ2222-2-22222222-2-2-2-2-2-2-22i2i−2i−2i00002i−2i000000000000-22000000−2i2i000000
χ2322-2-22222222-2-2-2-2-2-2-2−2i−2i2i2i0000−2i2i0000000000002-2000000−2i2i000000
χ2422-2-22222222-2-2-2-2-2-2-2−2i−2i2i2i0000−2i2i000000000000-220000002i−2i000000
χ2522-2-222-2-2-22-22-2222-2-200002i−2i2i−2i0000000200-20000000000000002i−2i00
χ2622-2-222-2-2-22-22-2222-2-200002i−2i2i−2i0000000-2002000000000000000−2i2i00
χ2722-2-222-2-2-22-22-2222-2-20000−2i2i−2i2i0000000200-2000000000000000−2i2i00
χ2822-2-222-2-2-22-22-2222-2-20000−2i2i−2i2i0000000-20020000000000000002i−2i00
χ2922-2-22-22-2-2-22-2222-22-200002i−2i−2i2i000000200-20000000000000000002i−2i
χ3022-2-22-22-2-2-22-2222-22-200002i−2i−2i2i000000-2002000000000000000000−2i2i
χ3122-2-22-22-2-2-22-2222-22-20000−2i2i2i−2i000000200-2000000000000000000−2i2i
χ3222-2-22-22-2-2-22-2222-22-20000−2i2i2i−2i000000-20020000000000000000002i−2i
χ3322-2-22-2-222-2-222-2-222-22i2i−2i−2i0000−2i2i000000000000002i−2i0000002-20000
χ3422-2-22-2-222-2-222-2-222-22i2i−2i−2i0000−2i2i00000000000000−2i2i000000-220000
χ3522-2-22-2-222-2-222-2-222-2−2i−2i2i2i00002i−2i000000000000002i−2i000000-220000
χ3622-2-22-2-222-2-222-2-222-2−2i−2i2i2i00002i−2i00000000000000−2i2i0000002-20000
χ3722-2-2-2222-2-2-2222-2-2-2200000000002-22-20000000000002i−2i2i−2i00000000
χ3822-2-2-2222-2-2-2222-2-2-2200000000002-22-2000000000000−2i2i−2i2i00000000
χ3922-2-2-2222-2-2-2222-2-2-220000000000-22-220000000000002i−2i−2i2i00000000
χ4022-2-2-2222-2-2-2222-2-2-220000000000-22-22000000000000−2i2i2i−2i00000000
χ4122-2-2-2-2-22-222-2-22-222200000000002-2-2200200-22-20000000000000000
χ4222-2-2-2-2-22-222-2-22-222200000000002-2-2200-2002-220000000000000000
χ4322-2-2-2-2-22-222-2-22-22220000000000-222-200200-2-220000000000000000
χ4422-2-2-2-2-22-222-2-22-22220000000000-222-200-20022-20000000000000000
χ45444444-4-4-44-4-44-4-4-44400000000000000000000000000000000000000
χ4644444-44-4-4-444-4-4-44-4400000000000000000000000000000000000000
χ474444-4444-4-4-4-4-4-4444-400000000000000000000000000000000000000
χ484444-44-4-44-444-44-4-44-400000000000000000000000000000000000000
χ494444-4-44-444-4-444-44-4-400000000000000000000000000000000000000
χ504444-4-4-44-44444-44-4-4-400000000000000000000000000000000000000
χ5144-4-4-44-4-44-44-44-444-4400000000000000000000000000000000000000
χ5244-4-4-4-44-444-44-4-44-44400000000000000000000000000000000000000
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.