Finite Group Databasebeta

← Group #479798

Character table — Group #479798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222222222888888888888161616161616161616161616161616161616161616161616
order12224444222222444444444488888888244444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111-111-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ6111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11-1-111111-1-1-1-1-1-11111-1-111-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-11111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1111111-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-111-1-1-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-111
χ172222-2-2-2-22-2-22-2-2222-2-2200002i2i−2i−2i000002-2000002i−2i00000000000000
χ182222-2-2-2-22-2-22-2-2222-2-2200002i2i−2i−2i00000-2200000−2i2i00000000000000
χ192222-2-2-2-22-2-22-2-2222-2-220000−2i−2i2i2i000002-200000−2i2i00000000000000
χ202222-2-2-2-22-2-22-2-2222-2-220000−2i−2i2i2i00000-22000002i−2i00000000000000
χ212222-2-2-2-2-22-2-22-22-2-222222-2-2000000000000000000002i−2i2i−2i00000000
χ222222-2-2-2-2-22-2-22-22-2-222222-2-200000000000000000000−2i2i−2i2i00000000
χ232222-2-2-2-2-22-2-22-22-2-2222-2-222000000000000000000002i−2i−2i2i00000000
χ242222-2-2-2-2-22-2-22-22-2-2222-2-22200000000000000000000−2i2i2i−2i00000000
χ252222-2-2-2-2-2-22-2-22-22222-2000000002i2i−2i−2i200-20000002i−2i000000000000
χ262222-2-2-2-2-2-22-2-22-22222-2000000002i2i−2i−2i-2002000000−2i2i000000000000
χ272222-2-2-2-2-2-22-2-22-22222-200000000−2i−2i2i2i200-2000000−2i2i000000000000
χ282222-2-2-2-2-2-22-2-22-22222-200000000−2i−2i2i2i-20020000002i−2i000000000000
χ292-2-2222-2-222-2-2-22-22-22-2200000000000000002-22i−2i0000000000002i−2i00
χ302-2-2222-2-222-2-2-22-22-22-2200000000000000002-2−2i2i000000000000−2i2i00
χ312-2-2222-2-222-2-2-22-22-22-220000000000000000-222i−2i000000000000−2i2i00
χ322-2-2222-2-222-2-2-22-22-22-220000000000000000-22−2i2i0000000000002i−2i00
χ332-2-22-2-22222-2-2-222-22-22-200000000000000000000000000002-22i−2i002i−2i
χ342-2-22-2-22222-2-2-222-22-22-200000000000000000000000000002-2−2i2i00−2i2i
χ352-2-22-2-22222-2-2-222-22-22-20000000000000000000000000000-222i−2i00−2i2i
χ362-2-22-2-22222-2-2-222-22-22-20000000000000000000000000000-22−2i2i002i−2i
χ37444444444-4-44-4-4-4-4-444-4000000000000000000000000000000000000
χ3844444444-44-4-44-4-444-4-4-4000000000000000000000000000000000000
χ3944444444-4-44-4-444-4-4-4-44000000000000000000000000000000000000
χ404444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000
χ4144-4-44i−4i4i−4i0000000000002-22i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ4244-4-44i−4i4i−4i0000000000002-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ4344-4-44i−4i4i−4i000000000000-22−2i2i2ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ4444-4-44i−4i4i−4i000000000000-22−2i2i−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ4544-4-4−4i4i−4i4i0000000000002-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ4644-4-4−4i4i−4i4i0000000000002-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ4744-4-4−4i4i−4i4i000000000000-222i−2i2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ4844-4-4−4i4i−4i4i000000000000-222i−2i−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ494-4-4444-4-44-44-44-44-444-4-4000000000000000000000000000000000000
χ504-4-4444-4-4-4444-4-444-4-44-4000000000000000000000000000000000000
χ514-4-4444-4-4-4-4-4444-4-44-444000000000000000000000000000000000000
χ524-4-44-4-4444-44-44-4-44-4-444000000000000000000000000000000000000
χ534-4-44-4-444-4444-4-4-4-444-44000000000000000000000000000000000000
χ544-4-44-4-444-4-4-444444-44-4-4000000000000000000000000000000000000
χ558-88-88i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000

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