Finite Group Databasebeta

← Group #489202

Character table — Group #489202

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222444444888844488884444444481616161616161616161616161616161622224488888822
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1
χ91111-1-1-1-1-1-111-1-1-1-1-11111111-11-111-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-11-1
χ101111-1-1-1-1-1-111-1-1-1-1-11111111-11-111-1-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-11
χ111111-1-1-1-1-1-111-1-1-1-1-11111111-11-1-1-111-11111-1-1-1-11111-1-1-1-1-11-11-111-1-1-111-11
χ121111-1-1-1-1-1-111-1-1-1-1-11111111-11-1-1-111-1-1-1-1-11111-1-1-1-11111-11-11-111-111-1-11-1
χ131111-1-1-1-1-1-111-1-1-1-1-1111111-11-1111-1-1-11111-1-1-1-1-1-1-1-111111-1-11-11-1111-1-1-11
χ141111-1-1-1-1-1-111-1-1-1-1-1111111-11-1111-1-1-1-1-1-1-111111111-1-1-1-11-1-11-11-11-1-1111-1
χ151111-1-1-1-1-1-111-1-1-1-1-1111111-11-11-1-111-11111-1-1-1-1-1-1-1-11111-111-11-1-11-1-1111-1
χ161111-1-1-1-1-1-111-1-1-1-1-1111111-11-11-1-111-1-1-1-1-111111111-1-1-1-1-111-11-1-1111-1-1-11
χ17222222222222-2-2-2-2222-2-2-2-222220000-20000000000000000000000-2-2000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-20000-2000000000000000000000022000000
χ1922222222-2-2222222-2-2-22-2-2200002222-20000000000000000-2-2000000000000
χ2022222222-2-2222222-2-2-22-2-220000-2-2-2-2-2000000000000000022000000000000
χ2122222222-2-222-2-2-2-2-2-2-2-222-20000000020000000000000000002-2-2200000000
χ2222222222-2-222-2-2-2-2-2-2-2-222-2000000002000000000000000000-222-200000000
χ23222222-2-2-2-2-2-200002-2200002-2-220000022−2−222−2−222−2−222−2−200000000000000
χ24222222-2-2-2-2-2-200002-2200002-2-2200000−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-2-2-2-2-200002-220000-222-20000022−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-2-2-2-2-200002-220000-222-200000−2−222−2−22222−2−222−2−200000000000000
χ272222-2-22222-2-20000-2-22000022-2-20000022−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-22222-2-20000-2-22000022-2-200000−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-22222-2-20000-2-220000-2-2220000022−2−2−2−222−2−22222−2−200000000000000
χ302222-2-22222-2-20000-2-220000-2-22200000−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-2222222222-2-2-222-200000000-200000000000000000022-2-200000000
χ322222-2-2-2-2222222222-2-2-222-200000000-2000000000000000000-2-22200000000
χ332222-2-2-2-22222-2-2-2-22-2-22-2-22000022-2-220000000000000000-22000000000000
χ342222-2-2-2-22222-2-2-2-22-2-22-2-220000-2-222200000000000000002-2000000000000
χ352222-2-2-2-2-2-2222222-222-2-2-2-22-22-2000020000000000000000000000-22000000
χ362222-2-2-2-2-2-2222222-222-2-2-2-2-22-220000200000000000000000000002-2000000
χ372-22-22-22-2002-222-2-2000200-200002i−2i2i−2i02−22−22−22−20000000000000000i2−i2i2−i200
χ382-22-22-22-2002-222-2-2000200-200002i−2i2i−2i0−22−22−22−220000000000000000−i2i2−i2i200
χ392-22-22-22-2002-222-2-2000200-20000−2i2i−2i2i02−22−22−22−20000000000000000−i2i2−i2i200
χ402-22-22-22-2002-222-2-2000200-20000−2i2i−2i2i0−22−22−22−220000000000000000i2−i2i2−i200
χ412-22-2-22-22002-2-2-222000200-200002i−2i−2i2i02−22−2−22−220000000000000000i2−i2−i2i200
χ422-22-2-22-22002-2-2-222000200-200002i−2i−2i2i0−22−222−22−20000000000000000−i2i2i2−i200
χ432-22-2-22-22002-2-2-222000200-20000−2i2i2i−2i02−22−2−22−220000000000000000−i2i2i2−i200
χ442-22-2-22-22002-2-2-222000200-20000−2i2i2i−2i0−22−222−22−20000000000000000i2−i2−i2i200
χ45444444-4-444-4-40000-44-40000000000000000000000000000000000000000000
χ464444-4-444-4-4-4-4000044-40000000000000000000000000000000000000000000
χ474-44-44-44-4004-4-4-444000-4004000000000000000000000000000000000000000
χ484-44-44-4-4400-44000000000000000000002-2-222-2-220000000000000000000000
χ494-44-44-4-4400-4400000000000000000000-222-2-222-20000000000000000000000
χ504-44-4-444-400-44000000000000000000002-2-22-222-20000000000000000000000
χ514-44-4-444-400-4400000000000000000000-222-22-2-220000000000000000000000
χ524-44-4-44-44004-444-4-4000-4004000000000000000000000000000000000000000
χ534-4-4400004-40022−2222−22000022−22000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ544-4-4400004-40022−2222−22000022−22000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ554-4-4400004-400−2222−22220000−2222000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ564-4-4400004-400−2222−22220000−2222000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ574-4-440000-440022−2222−220000−2222000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ584-4-440000-440022−2222−220000−2222000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ594-4-440000-4400−2222−2222000022−22000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ604-4-440000-4400−2222−2222000022−22000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
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.