Finite Group Databasebeta

← Group #239355

Character table — Group #239355

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444444444444444888888888888888844444444888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-11111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11-1-111-1-111-1-1
χ101111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-111-1-111-1-111
χ111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-1-1-111
χ121111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ131111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-11-1-1-111-1-11111-1-1
χ141111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11-1111-1-111-1-1-1-111
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1111-1-11-1-1-1-111-1-111
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-111-11111-1-111-1-1
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222222-2-2222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-2222222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ202222222222-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ2322222222-2-222-2-222-2-222-2-222-2-2-2-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-222-2-222-2-222-2-222-2-2-2-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-222-2-2-2-2-2-222-2-2-2-22222-22-220000000000000000000000000000000020-22-200000000000
χ2622222222-2-222-2-2-2-2-2-222-2-2-2-22222-22-2200000000000000000000000000000000-202-2200000000000
χ2722222222-2-2-2-22222-2-2-2-22222-2-2-2-2-22-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ2822222222-2-2-2-22222-2-2-2-22222-2-2-2-2-22-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ2922222222-2-2-2-222-2-2-2-2-2-222-2-222222-22-20000000000000000000000000000000002000-22-200000000
χ3022222222-2-2-2-222-2-2-2-2-2-222-2-222222-22-2000000000000000000000000000000000-20002-2200000000
χ312222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000022-2-2-2-222000000000000000000000000
χ322222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000-2-22222-2-2000000000000000000000000
χ332222-2-2-2-222-2-2-2-222-2-22222-2-2-2-222-2-22200000000000000000000000022-2-2-2-2220000000000000000
χ342222-2-2-2-222-2-2-2-222-2-22222-2-2-2-222-2-222000000000000000000000000-2-22222-2-20000000000000000
χ352222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-2-2-222-2-22222-2-222-2-222-2-22-2-22000000000000000000000000000000000000000000002i−2i−2i2i
χ382222-2-2-2-2-2-222-2-22222-2-222-2-222-2-22-2-2200000000000000000000000000000000000000000000−2i2i2i−2i
χ392222-2-2-2-2-2-222-2-2-2-222-2-22222-2-222-222-20000000000000000000000000000000020-2-2200000000000
χ402222-2-2-2-2-2-222-2-2-2-222-2-22222-2-222-222-200000000000000000000000000000000-2022-200000000000
χ412222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-222-200000000000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-222-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2222-2-220000000000000000000000000000000002000-2-2200000000
χ442222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2222-2-22000000000000000000000000000000000-200022-200000000
χ4522-2-22i2i−2i−2i2-22-22-2002i−2i2i−2i2i−2i0000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2002i−2i002-22−22−2i2−i2i2−i20000000000000000
χ4622-2-22i2i−2i−2i2-22-22-2002i−2i2i−2i2i−2i0000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200−2i2i00-22−22−22−i2i2−i2i20000000000000000
χ4722-2-22i2i−2i−2i2-22-22-2002i−2i2i−2i2i−2i0000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222002i−2i002-2−22−22−i2i2−i2i20000000000000000
χ4822-2-22i2i−2i−2i2-22-22-2002i−2i2i−2i2i−2i0000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200−2i2i00-222−22−2i2−i2i2−i20000000000000000
χ4922-2-22i2i−2i−2i2-2-22-22002i−2i−2i2i−2i2i000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i22-2002i−2i002−2−22i2−i2−i2i20000000000000000
χ5022-2-22i2i−2i−2i2-2-22-22002i−2i−2i2i−2i2i000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2-2200−2i2i00−222−2−i2i2i2−i20000000000000000
χ5122-2-22i2i−2i−2i2-2-22-22002i−2i−2i2i−2i2i0000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i22-2002i−2i00−222−2−i2i2i2−i20000000000000000
χ5222-2-22i2i−2i−2i2-2-22-22002i−2i−2i2i−2i2i0000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2-2200−2i2i002−2−22i2−i2−i2i20000000000000000
χ5322-2-2−2i−2i2i2i2-22-22-200−2i2i−2i2i−2i2i0000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222002i−2i00-222−22−2−i2i2−i2i20000000000000000
χ5422-2-2−2i−2i2i2i2-22-22-200−2i2i−2i2i−2i2i0000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200−2i2i002-2−22−22i2−i2i2−i20000000000000000
χ5522-2-2−2i−2i2i2i2-22-22-200−2i2i−2i2i−2i2i0000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2002i−2i00-22−22−22i2−i2i2−i20000000000000000
χ5622-2-2−2i−2i2i2i2-22-22-200−2i2i−2i2i−2i2i0000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−200−2i2i002-22−22−2−i2i2−i2i20000000000000000
χ5722-2-2−2i−2i2i2i2-2-22-2200−2i2i2i−2i2i−2i000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i22-200−2i2i002−2−22−i2i2i2−i20000000000000000
χ5822-2-2−2i−2i2i2i2-2-22-2200−2i2i2i−2i2i−2i000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2-22002i−2i00−222−2i2−i2−i2i20000000000000000
χ5922-2-2−2i−2i2i2i2-2-22-2200−2i2i2i−2i2i−2i0000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i22-200−2i2i00−222−2i2−i2−i2i20000000000000000
χ6022-2-2−2i−2i2i2i2-2-22-2200−2i2i2i−2i2i−2i0000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2-22002i−2i002−2−22−i2i2i2−i20000000000000000
χ6144-4-44i4i−4i−4i-444-4-4400−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ6244-4-44i4i−4i−4i-44-444-400−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ6344-4-4−4i−4i4i4i-444-4-44004i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ6444-4-4−4i−4i4i4i-44-444-4004i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ654-44-44-44-40000004i−4i0000004i−4i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ664-44-44-44-40000004i−4i0000004i−4i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ674-44-44-44-4000000−4i4i000000−4i4i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ684-44-44-44-4000000−4i4i000000−4i4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ694-44-4-44-440000004i−4i000000−4i4i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ704-44-4-44-440000004i−4i000000−4i4i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ714-44-4-44-44000000−4i4i0000004i−4i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ724-44-4-44-44000000−4i4i0000004i−4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ734-4-444i−4i−4i4i00000000000000004i−4i4-400002-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ744-4-444i−4i−4i4i00000000000000004i−4i4-40000-222-2-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ754-4-444i−4i−4i4i0000000000000000−4i4i-4400002i−2i−2i2i−2i2i2i−2i2-2-22-222-200000000000000000000000000000000
χ764-4-444i−4i−4i4i0000000000000000−4i4i-440000−2i2i2i−2i2i−2i−2i2i-222-22-2-2200000000000000000000000000000000
χ774-4-44−4i4i4i−4i00000000000000004i−4i-4400002i−2i−2i2i−2i2i2i−2i-222-22-2-2200000000000000000000000000000000
χ784-4-44−4i4i4i−4i00000000000000004i−4i-440000−2i2i2i−2i2i−2i−2i2i2-2-22-222-200000000000000000000000000000000
χ794-4-44−4i4i4i−4i0000000000000000−4i4i4-400002-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ804-4-44−4i4i4i−4i0000000000000000−4i4i4-40000-222-2-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000

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