Finite Group Databasebeta

← Group #489201

Character table — Group #489201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222444444888844488884444444481616161616161616161616161616161622244488888824
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
χ511111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-111-111-1-11111-1-1
χ91111-1-1-1-1-1-111-1-1-1-11-11111111-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-11-1
χ101111-1-1-1-1-1-111-1-1-1-11-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111-11
χ111111-1-1-1-1-1-111-1-1-1-11-11111111-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-111-111-1-1-111-11
χ121111-1-1-1-1-1-111-1-1-1-11-11111111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-111-111-111-1-11-1
χ131111-1-1-1-1-1-111-1-1-1-11-111111-1-11111-1-1-11111-1-1-1-1-1-1-1-111111-11-1-11-1111-1-1-11
χ141111-1-1-1-1-1-111-1-1-1-11-111111-1-11111-1-1-1-1-1-1-111111111-1-1-1-11-11-1-11-11-1-1111-1
χ151111-1-1-1-1-1-111-1-1-1-11-111111-1-111-1-111-11111-1-1-1-1-1-1-1-11111-11-111-1-11-1-1111-1
χ161111-1-1-1-1-1-111-1-1-1-11-111111-1-111-1-111-1-1-1-1-111111111-1-1-1-1-11-111-1-1111-1-1-11
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
χ1922222222-2-2-2-20000-2-2200002-22-20000022−2−222−2−222−2−222−2−200000000000000
χ2022222222-2-2-2-20000-2-2200002-22-200000−2−222−2−222−2−222−2−22200000000000000
χ2122222222-2-2-2-20000-2-220000-22-220000022−2−222−2−2−2−222−2−22200000000000000
χ2222222222-2-2-2-20000-2-220000-22-2200000−2−222−2−22222−2−222−2−200000000000000
χ23222222-2-222222222-2-2-22-2-2200002222-20000000000000000-200-20000000000
χ24222222-2-222222222-2-2-22-2-220000-2-2-2-2-2000000000000000020020000000000
χ25222222-2-22222-2-2-2-2-2-2-2-222-200000000200000000000000000220-2-200000000
χ26222222-2-22222-2-2-2-2-2-2-2-222-200000000200000000000000000-2-202200000000
χ272222-2-222-2-2222222-22-2-222-200000000-2000000000000000002-20-2200000000
χ282222-2-222-2-2222222-22-2-222-200000000-200000000000000000-2202-200000000
χ292222-2-222-2-222-2-2-2-2-22-22-2-22000022-2-220000000000000000-20020000000000
χ302222-2-222-2-222-2-2-2-2-22-22-2-220000-2-22220000000000000000200-20000000000
χ312222-2-2-2-222-2-20000-22200002-2-220000022−2−2−2−22222−2−2−2−22200000000000000
χ322222-2-2-2-222-2-20000-22200002-2-2200000−2−22222−2−2−2−22222−2−200000000000000
χ332222-2-2-2-222-2-20000-2220000-222-20000022−2−2−2−222−2−22222−2−200000000000000
χ342222-2-2-2-222-2-20000-2220000-222-200000−2−22222−2−222−2−2−2−22200000000000000
χ352222-2-2-2-2-2-22222222-22-2-2-2-222-2-2000020000000000000000000000-22000000
χ362222-2-2-2-2-2-22222222-22-2-2-2-2-2-2220000200000000000000000000002-2000000
χ372-2-222-2002-22-222-2-2000200-200002i−2i2i−2i02−22−22−22−20000000000000000i2−i2i2−i200
χ382-2-222-2002-22-222-2-2000200-200002i−2i2i−2i0−22−22−22−220000000000000000−i2i2−i2i200
χ392-2-222-2002-22-222-2-2000200-20000−2i2i−2i2i02−22−22−22−20000000000000000−i2i2−i2i200
χ402-2-222-2002-22-222-2-2000200-20000−2i2i−2i2i0−22−22−22−220000000000000000i2−i2i2−i200
χ412-2-22-2200-222-2-2-222000200-200002i−2i−2i2i02−22−2−22−220000000000000000i2−i2−i2i200
χ422-2-22-2200-222-2-2-222000200-200002i−2i−2i2i0−22−222−22−20000000000000000−i2i2i2−i200
χ432-2-22-2200-222-2-2-222000200-20000−2i2i2i−2i02−22−2−22−220000000000000000−i2i2i2−i200
χ442-2-22-2200-222-2-2-222000200-20000−2i2i2i−2i0−22−222−22−20000000000000000i2−i2−i2i200
χ45444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000
χ464444-4-44444-4-400004-4-40000000000000000000000000000000000000000000
χ4744-4-4004i−4i00002i2−2i22i2−2i2000022−22000000000000000000ζ+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
χ4844-4-4004i−4i00002i2−2i22i2−2i2000022−22000000000000000000−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
χ4944-4-4004i−4i0000−2i22i2−2i22i20000−2222000000000000000000ζ−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
χ5044-4-4004i−4i0000−2i22i2−2i22i20000−2222000000000000000000−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
χ5144-4-400−4i4i00002i2−2i22i2−2i20000−2222000000000000000000ζ−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
χ5244-4-400−4i4i00002i2−2i22i2−2i20000−2222000000000000000000−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
χ5344-4-400−4i4i0000−2i22i2−2i22i2000022−22000000000000000000ζ+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
χ5444-4-400−4i4i0000−2i22i2−2i22i2000022−22000000000000000000−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
χ554-4-444-4004-44-4-4-444000-4004000000000000000000000000000000000000000
χ564-4-444-400-44-44000000000000000000002-2-222-2-220000000000000000000000
χ574-4-444-400-44-4400000000000000000000-222-2-222-20000000000000000000000
χ584-4-44-44004-4-44000000000000000000002-2-22-222-20000000000000000000000
χ594-4-44-44004-4-4400000000000000000000-222-22-2-220000000000000000000000
χ604-4-44-4400-444-444-4-4000-4004000000000000000000000000000000000000000
χ618-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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