Finite Group Databasebeta

← Group #317007

Character table — Group #317007

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488884448888888888882244444444448888888888888888844884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-11
χ11111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111111111-1-111-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-11111-1-1111-1-11
χ1722222222-2-2222222-2-2-222-2-200000000000022-2-222-2-2-2000000000000000000000000
χ1822222222-2-2222222-2-2-222-2-2000000000000-2-222-2-222-2000000000000000000000000
χ1922222222-2-222-2-2-2-2-2-2-2-2-22200000000000022-2-2-2-2222000000000000000000000000
χ2022222222-2-222-2-2-2-2-2-2-2-2-222000000000000-2-22222-2-22000000000000000000000000
χ21222222-2-2-2-2-2-20000-22200002i2i2i2i−2i−2i−2i−2i22-2-20000000000000000000000000002i−2i0000
χ22222222-2-2-2-2-2-20000-22200002i2i2i2i−2i−2i−2i−2i-2-222000000000000000000000000000−2i2i0000
χ23222222-2-2-2-2-2-20000-2220000−2i−2i−2i−2i2i2i2i2i22-2-2000000000000000000000000000−2i2i0000
χ24222222-2-2-2-2-2-20000-2220000−2i−2i−2i−2i2i2i2i2i-2-2220000000000000000000000000002i−2i0000
χ252222-2-222-2-2-2-200002-2200002i2i−2i−2i2i2i−2i−2i00000000000002i2i−2i−2i0000000000002-2000000
χ262222-2-222-2-2-2-200002-2200002i2i−2i−2i2i2i−2i−2i0000000000000−2i−2i2i2i000000000000-22000000
χ272222-2-222-2-2-2-200002-220000−2i−2i2i2i−2i−2i2i2i00000000000002i2i−2i−2i000000000000-22000000
χ282222-2-222-2-2-2-200002-220000−2i−2i2i2i−2i−2i2i2i0000000000000−2i−2i2i2i0000000000002-2000000
χ292222-2-2-2-222222222-2-22-2-22222-2-2-2-222000000000000-200000000000022-2-200000000
χ302222-2-2-2-222222222-2-22-2-222-2-22222-2-2000000000000-2000000000000-2-22200000000
χ312222-2-2-2-22222-2-2-2-2-2-2222-2-222-2-2-2-2220000000000002000000000000-2-22200000000
χ322222-2-2-2-22222-2-2-2-2-2-2222-2-2-2-22222-2-2000000000000200000000000022-2-200000000
χ332222-2-2-2-2-2-222222222-2-2-2-2-200000000000000000000200002i2i−2i−2i2i2i−2i−2i000000000000
χ342222-2-2-2-2-2-222222222-2-2-2-2-20000000000000000000020000−2i−2i2i2i−2i−2i2i2i000000000000
χ352222-2-2-2-2-2-222-2-2-2-222-2222200000000000000000000-200002i2i−2i−2i−2i−2i2i2i000000000000
χ362222-2-2-2-2-2-222-2-2-2-222-2222200000000000000000000-20000−2i−2i2i2i2i2i−2i−2i000000000000
χ372-22-22-22-2002-22i2i−2i−2i0002i−2i002−22−22−22−20000002i−2i002-200000i2−i2i2−i22−22−2i2−i2i2−i200000000
χ382-22-22-22-2002-22i2i−2i−2i0002i−2i002−22−22−22−2000000−2i2i00-2200000−i2i2−i2i2−22−22i2−i2i2−i200000000
χ392-22-22-22-2002-22i2i−2i−2i0002i−2i00−22−22−22−220000002i−2i002-200000−i2i2−i2i2−22−22−i2i2−i2i200000000
χ402-22-22-22-2002-22i2i−2i−2i0002i−2i00−22−22−22−22000000−2i2i00-2200000i2−i2i2−i22−22−2−i2i2−i2i200000000
χ412-22-22-22-2002-2−2i−2i2i2i000−2i2i002−22−22−22−20000002i−2i00-2200000i2−i2i2−i2−22−22−i2i2−i2i200000000
χ422-22-22-22-2002-2−2i−2i2i2i000−2i2i002−22−22−22−2000000−2i2i002-200000−i2i2−i2i22−22−2−i2i2−i2i200000000
χ432-22-22-22-2002-2−2i−2i2i2i000−2i2i00−22−22−22−220000002i−2i00-2200000−i2i2−i2i22−22−2i2−i2i2−i200000000
χ442-22-22-22-2002-2−2i−2i2i2i000−2i2i00−22−22−22−22000000−2i2i002-200000i2−i2i2−i2−22−22i2−i2i2−i200000000
χ452-22-2-22-22002-22i2i−2i−2i000−2i2i002−2−22−222−200002-2002i−2i00000002−2−22−i2i2i2−i2i2−i2−i2i200000000
χ462-22-2-22-22002-22i2i−2i−2i000−2i2i002−2−22−222−20000-2200−2i2i0000000−222−2i2−i2−i2i2i2−i2−i2i200000000
χ472-22-2-22-22002-22i2i−2i−2i000−2i2i00−222−22−2−2200002-2002i−2i0000000−222−2i2−i2−i2i2−i2i2i2−i200000000
χ482-22-2-22-22002-22i2i−2i−2i000−2i2i00−222−22−2−220000-2200−2i2i00000002−2−22−i2i2i2−i2−i2i2i2−i200000000
χ492-22-2-22-22002-2−2i−2i2i2i0002i−2i002−2−22−222−200002-200−2i2i00000002−2−22i2−i2−i2i2−i2i2i2−i200000000
χ502-22-2-22-22002-2−2i−2i2i2i0002i−2i002−2−22−222−20000-22002i−2i0000000−222−2−i2i2i2−i2−i2i2i2−i200000000
χ512-22-2-22-22002-2−2i−2i2i2i0002i−2i00−222−22−2−2200002-200−2i2i0000000−222−2−i2i2i2−i2i2−i2−i2i200000000
χ522-22-2-22-22002-2−2i−2i2i2i0002i−2i00−222−22−2−220000-22002i−2i00000002−2−22i2−i2−i2i2i2−i2−i2i200000000
χ53444444-4-444-4-400004-4-40000000000000000000000000000000000000000000000000
χ544444-4-44444-4-40000-44-40000000000000000000000000000000000000000000000000
χ554-44-44-4-4400-44000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000
χ564-44-44-4-4400-4400000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000
χ574-44-4-444-400-44000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ584-44-4-444-400-4400000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ594-4-4400004i−4i002i2−2i22i2−2i20000022−22000000002-22i−2i0000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ604-4-4400004i−4i002i2−2i22i2−2i20000022−2200000000-22−2i2i000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ614-4-4400004i−4i00−2i22i2−2i22i200000−2222000000002-22i−2i000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ624-4-4400004i−4i00−2i22i2−2i22i200000−222200000000-22−2i2i0000000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ634-4-440000−4i4i002i2−2i22i2−2i200000−2222000000002-2−2i2i0000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ644-4-440000−4i4i002i2−2i22i2−2i200000−222200000000-222i−2i000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ654-4-440000−4i4i00−2i22i2−2i22i20000022−22000000002-2−2i2i000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ664-4-440000−4i4i00−2i22i2−2i22i20000022−2200000000-222i−2i0000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ6788-8-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ6888-8-800000000−424242−420000000000000000000000000000000000000000000000000000

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