Finite Group Databasebeta

← Group #490459

Character table — Group #490459

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488884448888888888882222444488888888888881616161616161616161616162444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-11-1-11
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ91111-1-1-1-111111111-1-1111-1-11111-1-1-1-111-1-111-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ101111-1-1-1-111111111-1-1111-1-11111-1-1-1-111-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111
χ111111-1-1-1-111111111-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111
χ121111-1-1-1-111111111-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1
χ131111-1-1-1-111111111-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-11-11
χ141111-1-1-1-111111111-1-1111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-11-11-1
χ151111-1-1-1-111111111-1-1111-1-1-1-1-1-11111-1-111-1-111-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111-11-1
χ161111-1-1-1-111111111-1-1111-1-1-1-1-1-11111-1-111-1-111-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-11-11
χ17222222222222-2-2-2-2222-2-2-2-22222222200000000-200000000-2-2-2-20000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-200000000-20000000022220000000000000000
χ192222222222-2-22222-2-2-2-2-222000000002222-2-2-2-2-20000000000000000000000000000
χ202222222222-2-22222-2-2-2-2-22200000000-2-2-2-22222-20000000000000000000000000000
χ212222222222-2-2-2-2-2-2-2-2-222-2-2000000000000000022i2i−2i−2i2i2i−2i−2i00000000000000000000
χ222222222222-2-2-2-2-2-2-2-2-222-2-200000000000000002−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ23222222-2-2-2-2220000-22-2000022-2-222-2-200000000000000000000022−2−222−2−22−22−20000
χ24222222-2-2-2-2220000-22-2000022-2-222-2-2000000000000000000000−2−222−2−222−22−220000
χ25222222-2-2-2-2220000-22-20000-2-222-2-22200000000000000000000022−2−222−2−2−22−220000
χ26222222-2-2-2-2220000-22-20000-2-222-2-222000000000000000000000−2−222−2−2222−22−20000
χ272222-2-222-2-22200002-2-2000022-2-2-2-22200000000000000000000022−2−2−2−2222−2−220000
χ282222-2-222-2-22200002-2-2000022-2-2-2-222000000000000000000000−2−22222−2−2−222−20000
χ292222-2-222-2-22200002-2-20000-2-22222-2-200000000000000000000022−2−2−2−222−222−20000
χ302222-2-222-2-22200002-2-20000-2-22222-2-2000000000000000000000−2−22222−2−22−2−220000
χ312222-2-2-2-22222-2-2-2-2-2-22-2-2222222-2-2-2-200000000200000000-2-2220000000000000000
χ322222-2-2-2-22222-2-2-2-2-2-22-2-222-2-2-2-222220000000020000000022-2-20000000000000000
χ332222-2-2-2-222-2-2222222-2-2-2-2-20000000022-2-2-2-22220000000000000000000000000000
χ342222-2-2-2-222-2-2222222-2-2-2-2-200000000-2-22222-2-220000000000000000000000000000
χ352222-2-2-2-222-2-2-2-2-2-222-222220000000000000000-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-222-222220000000000000000-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ372-2-222-22-22-20022-2-2000002-22−22−22−22−200002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ382-2-222-22-22-20022-2-2000002-22−22−22−22−20000−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i22−22−20000000000000000
χ392-2-222-22-22-20022-2-2000002-2−22−22−22−2200002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ402-2-222-22-22-20022-2-2000002-2−22−22−22−220000−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2−22−220000000000000000
χ412-2-222-22-22-200-2-22200000-222−22−22−22−22-22-2000002−2−222−2−22−22−220000000000000000
χ422-2-222-22-22-200-2-22200000-222−22−22−22−2-22-2200000−222−2−222−2−22−220000000000000000
χ432-2-222-22-22-200-2-22200000-22−22−22−22−222-22-200000−222−2−222−22−22−20000000000000000
χ442-2-222-22-22-200-2-22200000-22−22−22−22−22-22-22000002−2−222−2−222−22−20000000000000000
χ452-2-22-22-222-20022-2-200000-222−22−2−22−2200002i−2i−2i2i0i2−i2i2−i2−i2i2−i2i22−2−220000000000000000
χ462-2-22-22-222-20022-2-200000-222−22−2−22−220000−2i2i2i−2i0−i2i2−i2i2i2−i2i2−i22−2−220000000000000000
χ472-2-22-22-222-20022-2-200000-22−22−222−22−200002i−2i−2i2i0−i2i2−i2i2i2−i2i2−i2−222−20000000000000000
χ482-2-22-22-222-20022-2-200000-22−22−222−22−20000−2i2i2i−2i0i2−i2i2−i2−i2i2−i2i2−222−20000000000000000
χ492-2-22-22-222-200-2-222000002-22−22−2−22−222-2-22000002−2−22−222−2−222−20000000000000000
χ502-2-22-22-222-200-2-222000002-22−22−2−22−22-222-200000−222−22−2−22−222−20000000000000000
χ512-2-22-22-222-200-2-222000002-2−22−222−22−22-2-2200000−222−22−2−222−2−220000000000000000
χ522-2-22-22-222-200-2-222000002-2−22−222−22−2-222-2000002−2−22−222−22−2−220000000000000000
χ53444444-4-4-4-4-4-400004-440000000000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-40000-4440000000000000000000000000000000000000000000000000
χ554-44-40000004-422−2222−2200022−22000000000000000000000000000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000
χ564-44-40000004-422−2222−2200022−2200000000000000000000000000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000
χ574-44-40000004-4−2222−2222000−2222000000000000000000000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000
χ584-44-40000004-4−2222−2222000−222200000000000000000000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000
χ594-44-4000000-4422−2222−22000−222200000000000000000000000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000
χ604-44-4000000-4422−2222−22000−22220000000000000000000000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000
χ614-44-4000000-44−2222−222200022−2200000000000000000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000000000
χ624-44-4000000-44−2222−222200022−220000000000000000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000000000
χ634-4-444-4-44-44000000000000022−22−222222−22−22220000000000000000000000000000000000000
χ644-4-444-4-44-440000000000000−222222−22−222222−220000000000000000000000000000000000000
χ654-4-44-444-4-44000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ664-4-44-444-4-440000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ6788-8-80000000042−42−42420000000000000000000000000000000000000000000000000000
χ6888-8-800000000−424242−420000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.