Finite Group Databasebeta

← Group #232802

Character table — Group #232802

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222244444444444424444488888888888888888888888888888888222444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111-1-1-1111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111111-1-1-1
χ91111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-11-1-1
χ101111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-1-111-111
χ111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1111-1-1-111
χ121111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11-111-1111-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-111-111
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1111-1-11-1-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-1-1111-1-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-11-1-11-1-1-111
χ1722222222222222-2-2-2-2-2-2-2-2222-2-22-2-20000000022-2-222-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2222-2-22-2-200000000-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-2-22222222222-2-2-2-2-2-20000000022-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-2-22222222222-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000
χ2122222222-2-222222222-2-2-2-2-2-2-22-2-22-200000000000000000000000022-2-222-2-2000000000000
χ2222222222-2-222222222-2-2-2-2-2-2-22-2-22-2000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-22222-2-2-2-22222-2-2-2-22-2-22000000000000000022-2-222-2-200000000000000000000
χ2422222222-2-22222-2-2-2-22222-2-2-2-22-2-220000000000000000-2-222-2-22200000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-22-222-22000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-22-222-220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-222-222-200000000000000000000000022-2-2-2-222000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-222-222-2000000000000000000000000-2-22222-2-2000000000000
χ292222-2-2-2-22222-2-222-2-222-2-2-2-2222-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ302222-2-2-2-22222-2-222-2-222-2-2-2-2222-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ312222-2-2-2-22222-2-2-2-222-2-222-2-22-2-2-22200000000000000000000000000000000200-22-2000000
χ322222-2-2-2-22222-2-2-2-222-2-222-2-22-2-2-22200000000000000000000000000000000-2002-22000000
χ332222-2-2-2-222-2-22222-2-222-2-2-2-2-2-2-222200000000000000000000000000000000200-2-22000000
χ342222-2-2-2-222-2-22222-2-222-2-2-2-2-2-2-222200000000000000000000000000000000-20022-2000000
χ352222-2-2-2-222-2-222-2-222-2-222-2-2-2222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ362222-2-2-2-222-2-222-2-222-2-222-2-2-2222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ372222-2-2-2-2-2-222-2-222-2-2-2-22222-22-22-2200000000000000000000000000000000002000000-22-2
χ382222-2-2-2-2-2-222-2-222-2-2-2-22222-22-22-220000000000000000000000000000000000-20000002-22
χ392222-2-2-2-2-2-222-2-2-2-22222-2-222-2-2222-200000000000000000000000000000000020000-22-2000
χ402222-2-2-2-2-2-222-2-2-2-22222-2-222-2-2222-2000000000000000000000000000000000-200002-22000
χ412222-2-2-2-2-2-2-2-22222-2-2-2-222222-22-22-200000000000000000000000000000000020000-2-22000
χ422222-2-2-2-2-2-2-2-22222-2-2-2-222222-22-22-2000000000000000000000000000000000-2000022-2000
χ432222-2-2-2-2-2-2-2-222-2-22222-2-22222-2-2-2200000000000000000000000000000000002000000-2-22
χ442222-2-2-2-2-2-2-2-222-2-22222-2-22222-2-2-220000000000000000000000000000000000-200000022-2
χ4522-2-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-200000000000000002-22i−2i002−22−2i2−i2i2−i22−22−2i2−i2i2−i2000000000000
χ4622-2-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-200000000000000002-22i−2i00−22−22−i2i2−i2i2−22−22−i2i2−i2i2000000000000
χ4722-2-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-20000000000000000-22−2i2i002−22−2i2−i2i2−i2−22−22−i2i2−i2i2000000000000
χ4822-2-222-2-22-200002i−2i2i−2i2i−2i2i−2i2-20000000000000000-22−2i2i00−22−22−i2i2−i2i22−22−2i2−i2i2−i2000000000000
χ4922-2-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-200000000000000002-2−2i2i002−22−2−i2i2−i2i22−22−2−i2i2−i2i2000000000000
χ5022-2-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-200000000000000002-2−2i2i00−22−22i2−i2i2−i2−22−22i2−i2i2−i2000000000000
χ5122-2-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-20000000000000000-222i−2i002−22−2−i2i2−i2i2−22−22i2−i2i2−i2000000000000
χ5222-2-222-2-22-20000−2i2i−2i2i−2i2i−2i2i2-20000000000000000-222i−2i00−22−22i2−i2i2−i22−22−2−i2i2−i2i2000000000000
χ5322-2-222-2-2-2200002i−2i2i−2i−2i2i−2i2i-22000000000000002-200002i−2i2−2−22−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ5422-2-222-2-2-2200002i−2i2i−2i−2i2i−2i2i-22000000000000002-200002i−2i−222−2i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ5522-2-222-2-2-2200002i−2i2i−2i−2i2i−2i2i-2200000000000000-220000−2i2i2−2−22−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ5622-2-222-2-2-2200002i−2i2i−2i−2i2i−2i2i-2200000000000000-220000−2i2i−222−2i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ5722-2-222-2-2-220000−2i2i−2i2i2i−2i2i−2i-22000000000000002-20000−2i2i2−2−22i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ5822-2-222-2-2-220000−2i2i−2i2i2i−2i2i−2i-22000000000000002-20000−2i2i−222−2−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ5922-2-222-2-2-220000−2i2i−2i2i2i−2i2i−2i-2200000000000000-2200002i−2i2−2−22i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ6022-2-222-2-2-220000−2i2i−2i2i2i−2i2i−2i-2200000000000000-2200002i−2i−222−2−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ6144-4-4-4-4444-400004i−4i−4i4i4i−4i−4i4i-4400000000000000000000000000000000000000000000000000
χ6244-4-4-4-4444-40000−4i4i4i−4i−4i4i4i−4i-4400000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-4400004i−4i−4i4i−4i4i4i−4i4-400000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-440000−4i4i4i−4i4i−4i−4i4i4-400000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i004-44i−4i00000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000
χ664-44-44i−4i4i−4i004-44i−4i0000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000
χ674-44-44i−4i4i−4i00-44−4i4i00000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000
χ684-44-44i−4i4i−4i00-44−4i4i0000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000
χ694-44-4−4i4i−4i4i004-4−4i4i00000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000
χ704-44-4−4i4i−4i4i004-4−4i4i0000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i00-444i−4i00000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i00-444i−4i0000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000
χ738-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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