Finite Group Databasebeta

← Group #118293

Character table — Group #118293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444888888888888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-111-1-1-1-1-1-11-1-111-1-11iiii−i−i−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-111-1-1-1-1-1-11-1-111-1-11iiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−i
χ1111111111-1-111-1-1-1-1-1-11-1-111-1-11iiii−i−i−i−i-1-1-1-1111111-1-1-1-111ii−i−i−i−iii−i−iii
χ1211111111-1-111-1-1-1-1-1-11-1-111-1-11iiii−i−i−i−i-1-1-1-11111-1-11111-1-1−i−iiiii−i−i−i−iii
χ1311111111-1-111-1-1-1-1-1-11-1-111-1-11−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii
χ1411111111-1-111-1-1-1-1-1-11-1-111-1-11−i−i−i−iiiii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii
χ1511111111-1-111-1-1-1-1-1-11-1-111-1-11−i−i−i−iiiii-1-1-1-1111111-1-1-1-111−i−iiiii−i−iii−i−i
χ1611111111-1-111-1-1-1-1-1-11-1-111-1-11−i−i−i−iiiii-1-1-1-11111-1-11111-1-1ii−i−i−i−iiiii−i−i
χ172222222222-2-222-2-2-2-2222-2-2-2-2-200000000000000000000000000002i−2i2i−2i0000
χ182222222222-2-222-2-2-2-2222-2-2-2-2-20000000000000000000000000000−2i2i−2i2i0000
χ1922222222-2-2-2-2-2-222222-2-2-2-222-200000000000000000000000000002-2-220000
χ2022222222-2-2-2-2-2-222222-2-2-2-222-20000000000000000000000000000-222-20000
χ21222222-2-22222-2-22222-22-2-2-2-2-22000000000000000000000000000000002-22-2
χ22222222-2-22222-2-22222-22-2-2-2-2-2200000000000000000000000000000000-22-22
χ23222222-2-222-2-2-2-2-2-2-2-2-22-22222-200000000000000002-22-20000000000000000
χ24222222-2-222-2-2-2-2-2-2-2-2-22-22222-20000000000000000-22-220000000000000000
χ25222222-2-2-2-22222-2-2-2-2-2-22-2-2222000000000000000000000000000000002i−2i−2i2i
χ26222222-2-2-2-22222-2-2-2-2-2-22-2-222200000000000000000000000000000000−2i2i2i−2i
χ27222222-2-2-2-2-2-2222222-2-2222-2-2-200000000000000002-2-220000000000000000
χ28222222-2-2-2-2-2-2222222-2-2222-2-2-20000000000000000-222-20000000000000000
χ292222-2-222222222-2-222-2-2-22-22-2-20000000000000000000000002-22-200000000
χ302222-2-222222222-2-222-2-2-22-22-2-2000000000000000000000000-22-2200000000
χ312222-2-22222-2-22222-2-2-2-2-2-22-2220000000022-2-222-2-200000000000000000000
χ322222-2-22222-2-22222-2-2-2-2-2-22-22200000000-2-222-2-22200000000000000000000
χ332222-2-222-2-222-2-222-2-2-2222-2-22-20000000000000000000000002i−2i−2i2i00000000
χ342222-2-222-2-222-2-222-2-2-2222-2-22-2000000000000000000000000−2i2i2i−2i00000000
χ352222-2-222-2-2-2-2-2-2-2-222-222-222-220000000022-2-2-2-22200000000000000000000
χ362222-2-222-2-2-2-2-2-2-2-222-222-222-2200000000-2-22222-2-200000000000000000000
χ372222-2-2-2-22222-2-2-2-2222-22-22-22-2000000000000000000002i−2i2i−2i000000000000
χ382222-2-2-2-22222-2-2-2-2222-22-22-22-200000000000000000000−2i2i−2i2i000000000000
χ392222-2-2-2-222-2-2-2-222-2-22-222-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ402222-2-2-2-222-2-2-2-222-2-22-222-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ412222-2-2-2-2-2-2222222-2-222-2-222-2-2000000000000000000002i−2i−2i2i000000000000
χ422222-2-2-2-2-2-2222222-2-222-2-222-2-200000000000000000000−2i2i2i−2i000000000000
χ432222-2-2-2-2-2-2-2-222-2-22222-22-2-22222-2-2-2-2220000000000000000000000000000
χ442222-2-2-2-2-2-2-2-222-2-22222-22-2-222-2-22222-2-20000000000000000000000000000
χ4544-4-4004-44-4004-4000000000000000000000022−220022−2200000000000000000000
χ4644-4-4004-44-4004-40000000000000000000000−222200−222200000000000000000000
χ4744-4-4004-4-4400-44000000000000000000000022−2200−222200000000000000000000
χ4844-4-4004-4-4400-440000000000000000000000−22220022−2200000000000000000000
χ4944-4-400-444-400-44000000000000000000002i2−2i2002i2−2i20000000000000000000000
χ5044-4-400-444-400-4400000000000000000000−2i22i200−2i22i20000000000000000000000
χ5144-4-400-44-44004-4000000000000000000002i2−2i200−2i22i20000000000000000000000
χ5244-4-400-44-44004-400000000000000000000−2i22i2002i2−2i20000000000000000000000
χ534-44-44-4000000004i−4i4i−4i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000
χ544-44-44-4000000004i−4i4i−4i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000
χ554-44-44-400000000−4i4i−4i4i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000
χ564-44-44-400000000−4i4i−4i4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000
χ574-44-4-44000000004i−4i−4i4i000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000000000
χ584-44-4-44000000004i−4i−4i4i00000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000000000000000
χ594-44-4-4400000000−4i4i4i−4i000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000000000
χ604-44-4-4400000000−4i4i4i−4i00000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000000000
χ618-8-880000008i−8i00000000000000000000000000000000000000000000000000
χ628-8-88000000−8i8i00000000000000000000000000000000000000000000000000

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