Finite Group Databasebeta

← Group #239299

Character table — Group #239299

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12224444224444442244444444888888888888888822244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-111-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-11111
χ91111111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-111-111-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-1-11-11-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-111-11-1-1-111-1-11111-1-1
χ121111111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-1-1111-1-111-1-1-1-111
χ131111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-111-11-111-1-1-1-111-1-111
χ141111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-11-1-11111-1-111-1-1
χ151111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-111-1-1-11111-1-1-1-111
χ161111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1-11-1111-1-1-1-11111-1-1
χ172222222222222222-2-2-2-222-2-2-2-200000000000000000000000000002-22-20000
χ182222222222222222-2-2-2-222-2-2-2-20000000000000000000000000000-22-220000
χ192222222222-2-2-2-22222-2-2-2-222-2-200000000000000000000000000002-2-220000
χ202222222222-2-2-2-22222-2-2-2-222-2-20000000000000000000000000000-222-20000
χ2122222222-2-22222-2-22-22-2-2-22-22-2000000000000000000000000000000002i−2i2i−2i
χ2222222222-2-22222-2-22-22-2-2-22-22-200000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-22222-2-2-22-22-2-2-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2422222222-2-22222-2-2-22-22-2-2-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-2-22222-2-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2622222222-2-2-2-2-2-2-2-22-2-22222-2-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-222-222-222-2000000000000000000000000000000002i−2i−2i2i
χ2822222222-2-2-2-2-2-2-2-2-222-222-222-200000000000000000000000000000000−2i2i2i−2i
χ292222-2-2-2-22222-2-2-2-222222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ302222-2-2-2-22222-2-2-2-222222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ312222-2-2-2-22222-2-2-2-2-2-2-2-22-222220000000000000000000000002-22-200000000
χ322222-2-2-2-22222-2-2-2-2-2-2-2-22-22222000000000000000000000000-22-2200000000
χ332222-2-2-2-222-2-222-2-222-2-2-22-2-2220000000000000000000000002-2-2200000000
χ342222-2-2-2-222-2-222-2-222-2-2-22-2-222000000000000000000000000-222-200000000
χ352222-2-2-2-222-2-222-2-2-2-222-2222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362222-2-2-2-222-2-222-2-2-2-222-2222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372222-2-2-2-2-2-222-2-2222-22-2-22-22-22000000000000000002-2000-22000000000000
χ382222-2-2-2-2-2-222-2-2222-22-2-22-22-2200000000000000000-220002-2000000000000
χ392222-2-2-2-2-2-222-2-222-22-22-222-22-200000000000000002002-2-200000000000000
χ402222-2-2-2-2-2-222-2-222-22-22-222-22-20000000000000000-200-22200000000000000
χ412222-2-2-2-2-2-2-2-222222-2-222-2-222-20000000000000000200-22-200000000000000
χ422222-2-2-2-2-2-2-2-222222-2-222-2-222-20000000000000000-2002-2200000000000000
χ432222-2-2-2-2-2-2-2-22222-222-22-22-2-220000000000000000022000-2-2000000000000
χ442222-2-2-2-2-2-2-2-22222-222-22-22-2-2200000000000000000-2-200022000000000000
χ4544-4-44i4i−4i−4i004i−4i4-40000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ4644-4-44i4i−4i−4i004i−4i4-4000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ4744-4-44i4i−4i−4i00−4i4i-440000000000002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ4844-4-44i4i−4i−4i00−4i4i-44000000000000−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ4944-4-4−4i−4i4i4i004i−4i-440000000000002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ5044-4-4−4i−4i4i4i004i−4i-44000000000000−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ5144-4-4−4i−4i4i4i00−4i4i4-40000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ5244-4-4−4i−4i4i4i00−4i4i4-4000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ534-4-444-44-44-400004-400000000000000000000002i2−2i22i2−2i200000000000000000000
χ544-4-444-44-44-400004-40000000000000000000000−2i22i2−2i22i200000000000000000000
χ554-4-444-44-4-440000-44000000000000000000000022−22−222200000000000000000000
χ564-4-444-44-4-440000-440000000000000000000000−222222−2200000000000000000000
χ574-4-44-44-444-40000-440000000000000000002i2−2i22i2−2i2000000000000000000000000
χ584-4-44-44-444-40000-44000000000000000000−2i22i2−2i22i2000000000000000000000000
χ594-4-44-44-44-4400004-400000000000000000022−22−2222000000000000000000000000
χ604-4-44-44-44-4400004-4000000000000000000−222222−22000000000000000000000000
χ618-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000

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