Finite Group Databasebeta

← Group #489313

Character table — Group #489313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122244444444888824488882224444481616161616161616161616161616161624444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111-1-111-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ511111111111111111111111-1-111-1-11111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ91111-1-1-1-111111111-11-1-1-111111-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1111-1-11-111-1-11-1
χ101111-1-1-1-111111111-11-1-1-111111-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1111-1-11-1-1-111-11
χ111111-1-1-1-111111111-11-1-1-11111-11-1-1-11-11111-1-1-1-1-1-1-1-11111-11-1-111-11-1-1111-1
χ121111-1-1-1-111111111-11-1-1-11111-11-1-1-11-1-1-1-1-111111111-1-1-1-1-11-1-111-1111-1-1-11
χ131111-1-1-1-111111111-11-1-1-111-1-11-1111-1-11111-1-1-1-11111-1-1-1-11-1-1-1111-1-1-111-11
χ141111-1-1-1-111111111-11-1-1-111-1-11-1111-1-1-1-1-1-11111-1-1-1-111111-1-1-1111-111-1-11-1
χ151111-1-1-1-111111111-11-1-1-111-1-1-1111-11-11111-1-1-1-1-1-1-1-111111-111-1-1-1111-1-1-11
χ161111-1-1-1-111111111-11-1-1-111-1-1-1111-11-1-1-1-1-111111111-1-1-1-11-111-1-1-11-1-1111-1
χ17222222222222-2-2-2-2222-2-2-2-200220022-20000000000000000000000-2-2000000
χ18222222222222-2-2-2-2222-2-2-2-200-2-200-2-2-2000000000000000000000022000000
χ192222222222-2-22222-2-2-222-2-222002200-20000000000000000-2-2000000000000
χ202222222222-2-22222-2-2-222-2-2-2-200-2-200-2000000000000000022000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-2-2220000000020000000000000000002-22-200000000
χ222222222222-2-2-2-2-2-2-2-2-2-2-222000000002000000000000000000-22-2200000000
χ23222222-2-2-2-2220000-2-220000002-200-22022−2−222−2−222−2−222−2−200000000000000
χ24222222-2-2-2-2220000-2-220000002-200-220−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-2-2-2220000-2-22000000-22002-2022−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-2-2-2220000-2-22000000-22002-20−2−222−2−22222−2−222−2−200000000000000
χ272222-2-222-2-22200002-2-20000002200-2-2022−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-222-2-22200002-2-20000002200-2-20−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-222-2-22200002-2-2000000-2-20022022−2−2−2−222−2−22222−2−200000000000000
χ302222-2-222-2-22200002-2-2000000-2-200220−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-22222-2-2-2-2-22-222-2-2002-2002-220000000000000000000000-22000000
χ322222-2-2-2-22222-2-2-2-2-22-222-2-200-2200-22200000000000000000000002-2000000
χ332222-2-2-2-222-2-222222-22-2-2-2-22200-2-200200000000000000002-2000000000000
χ342222-2-2-2-222-2-222222-22-2-2-2-2-2-200220020000000000000000-22000000000000
χ352222-2-2-2-222-2-2-2-2-2-22-22222200000000-20000000000000000002-2-2200000000
χ362222-2-2-2-222-2-2-2-2-2-22-22222200000000-2000000000000000000-222-200000000
χ372-22-22i−2i2i−2i2-20022-2-20002i−2i002-2002i−2i00000000000i2−i2i2−i22−22−200000000i2−i22−200
χ382-22-22i−2i2i−2i2-20022-2-20002i−2i002-2002i−2i00000000000−i2i2−i2i2−22−2200000000−i2i2−2200
χ392-22-22i−2i2i−2i2-20022-2-20002i−2i00-2200−2i2i00000000000i2−i2i2−i22−22−200000000−i2i2−2200
χ402-22-22i−2i2i−2i2-20022-2-20002i−2i00-2200−2i2i00000000000−i2i2−i2i2−22−2200000000i2−i22−200
χ412-22-2−2i2i−2i2i2-20022-2-2000−2i2i002-200−2i2i00000000000i2−i2i2−i2−22−2200000000i2−i2−2200
χ422-22-2−2i2i−2i2i2-20022-2-2000−2i2i002-200−2i2i00000000000−i2i2−i2i22−22−200000000−i2i22−200
χ432-22-2−2i2i−2i2i2-20022-2-2000−2i2i00-22002i−2i00000000000i2−i2i2−i2−22−2200000000−i2i22−200
χ442-22-2−2i2i−2i2i2-20022-2-2000−2i2i00-22002i−2i00000000000−i2i2−i2i22−22−200000000i2−i2−2200
χ45444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000
χ464444-4-444-4-4-4-40000-4440000000000000000000000000000000000000000000
χ474-44-44i−4i4i−4i4-400-4-444000−4i4i00000000000000000000000000000000000000000
χ484-44-44i−4i−4i4i-440000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ494-44-44i−4i−4i4i-44000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ504-44-4−4i4i4i−4i-440000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ514-44-4−4i4i4i−4i-44000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ524-44-4−4i4i−4i4i4-400-4-4440004i−4i00000000000000000000000000000000000000000
χ534-4-440000004-422−2222−220000022−2200000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000
χ544-4-440000004-422−2222−220000022−220000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000
χ554-4-440000004-4−2222−222200000−222200000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000
χ564-4-440000004-4−2222−222200000−22220000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000
χ574-4-44000000-4422−2222−2200000−22220000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
χ584-4-44000000-4422−2222−2200000−2222000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ594-4-44000000-44−2222−22220000022−220000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ604-4-44000000-44−2222−22220000022−22000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ6188-8-80000000042−42−42420000000000000000000000000000000000000000000000
χ6288-8-800000000−424242−420000000000000000000000000000000000000000000000

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