Finite Group Databasebeta

← Group #489227

Character table — Group #489227

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222444444888844488884444444481616161616161616161616161616161622222488888844
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
χ511111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-111
χ611111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-11111-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-111
χ91111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-11-1
χ101111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-11-1-1-111-11
χ111111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-111-11
χ121111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-11111-111-1-11-1
χ131111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-11-1-1111-1
χ141111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-1111-1-1-11
χ151111-1-1-1-1111111111-1-1-1-111-1-111-1-111-11111-1-1-1-1-1-1-1-11111-111-1-11-1111-1-1-11
χ161111-1-1-1-1111111111-1-1-1-111-1-111-1-111-1-1-1-1-111111111-1-1-1-1-111-1-11-11-1-1111-1
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
χ1922222222-222-22222-2-2-222-2-200002222-20000000000000000-20000-200000000
χ2022222222-222-22222-2-2-222-2-20000-2-2-2-2-2000000000000000020000200000000
χ2122222222-222-2-2-2-2-2-2-2-2-2-222000000002000000000000000002-22-2000000000
χ2222222222-222-2-2-2-2-2-2-2-2-2-22200000000200000000000000000-22-22000000000
χ23222222-2-22-2-220000-22-200002-22-20000022−2−222−2−222−2−222−2−200000000000000
χ24222222-2-22-2-220000-22-200002-22-200000−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-22-2-220000-22-20000-22-220000022−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-22-2-220000-22-20000-22-2200000−2−222−2−22222−2−222−2−200000000000000
χ272222-2-2222-2-220000-2-2200002-2-220000022−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-2222-2-220000-2-2200002-2-2200000−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-2222-2-220000-2-220000-222-20000022−2−2−2−222−2−22222−2−200000000000000
χ302222-2-2222-2-220000-2-220000-222-200000−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-22222-2-2-2-22-2-222-2-222-2-2000020000000000000000000000-22000000
χ322222-2-2-2-22222-2-2-2-22-2-222-2-2-2-2220000200000000000000000000002-2000000
χ332222-2-2-2-2-222-22222-222-2-2-2-2000022-2-220000000000000000-20000200000000
χ342222-2-2-2-2-222-22222-222-2-2-2-20000-2-2222000000000000000020000-200000000
χ352222-2-2-2-2-222-2-2-2-2-2-222222200000000-2000000000000000002-2-22000000000
χ362222-2-2-2-2-222-2-2-2-2-2-222222200000000-200000000000000000-222-2000000000
χ3722-2-22-22-202-20-2-2220002-20000002i−2i2i−2i000000000i2−i2i2−i2i2−i2i2−i2000000002−22−200
χ3822-2-22-22-202-20-2-2220002-20000002i−2i2i−2i000000000−i2i2−i2i2−i2i2−i2i200000000−22−2200
χ3922-2-22-22-202-20-2-2220002-2000000−2i2i−2i2i000000000i2−i2i2−i2i2−i2i2−i200000000−22−2200
χ4022-2-22-22-202-20-2-2220002-2000000−2i2i−2i2i000000000−i2i2−i2i2−i2i2−i2i2000000002−22−200
χ4122-2-2-22-2202-20-2-222000-220000002i−2i−2i2i000000000i2−i2i2−i2−i2i2−i2i2000000002−2−2200
χ4222-2-2-22-2202-20-2-222000-220000002i−2i−2i2i000000000−i2i2−i2i2i2−i2i2−i200000000−222−200
χ4322-2-2-22-2202-20-2-222000-22000000−2i2i2i−2i000000000i2−i2i2−i2−i2i2−i2i200000000−222−200
χ4422-2-2-22-2202-20-2-222000-22000000−2i2i2i−2i000000000−i2i2−i2i2i2−i2i2−i2000000002−2−2200
χ45444444-4-4-4-4-4-400004-440000000000000000000000000000000000000000000
χ464444-4-444-4-4-4-4000044-40000000000000000000000000000000000000000000
χ4744-4-44-44-404-4044-4-4000-4400000000000000000000000000000000000000000
χ4844-4-44-4-440-44000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ4944-4-44-4-440-4400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5044-4-4-444-40-44000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ5144-4-4-444-40-4400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5244-4-4-44-4404-4044-4-40004-400000000000000000000000000000000000000000
χ534-44-40000400-422−2222−220000022−2200000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000
χ544-44-40000400-422−2222−220000022−220000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000
χ554-44-40000400-4−2222−222200000−222200000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000
χ564-44-40000400-4−2222−222200000−22220000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000
χ574-44-40000-400422−2222−2200000−22220000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ584-44-40000-400422−2222−2200000−2222000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ594-44-40000-4004−2222−22220000022−220000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ604-44-40000-4004−2222−22220000022−22000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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