Finite Group Databasebeta

← Group #489111

Character table — Group #489111

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122222444444888844488882244444481616161616161616161616161616161624444488888844
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
χ91111-1-1-1-1-1-111-1-1-1-11-1111111-11-111-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-111-1-11-1
χ101111-1-1-1-1-1-111-1-1-1-11-1111111-11-111-1-1-1-1-1-1-11111-1-1-1-111111-111-1-11-1-1-111-11
χ111111-1-1-1-1-1-111-1-1-1-11-1111111-11-1-1-111-11111-1-1-1-11111-1-1-1-1-11-1-1111-1-1-111-11
χ121111-1-1-1-1-1-111-1-1-1-11-1111111-11-1-1-111-1-1-1-1-11111-1-1-1-11111-11-1-1111-111-1-11-1
χ131111-1-1-1-1-1-111-1-1-1-11-111111-11-1111-1-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1111-1-1-11
χ141111-1-1-1-1-1-111-1-1-1-11-111111-11-1111-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111-11-1-1111-1
χ151111-1-1-1-1-1-111-1-1-1-11-111111-11-11-1-111-11111-1-1-1-1-1-1-1-11111-1111-1-1-11-1-1111-1
χ161111-1-1-1-1-1-111-1-1-1-11-111111-11-11-1-111-1-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1-11
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
χ2122222222-2-222-2-2-2-2-2-2-2-222-20000000020000000000000000002-22-200000000
χ2222222222-2-222-2-2-2-2-2-2-2-222-2000000002000000000000000000-22-2200000000
χ23222222-2-222-2-20000-2-2200002-2-220000022−2−222−2−222−2−222−2−200000000000000
χ24222222-2-222-2-20000-2-2200002-2-2200000−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-222-2-20000-2-220000-222-20000022−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-222-2-20000-2-220000-222-200000−2−222−2−22222−2−222−2−200000000000000
χ272222-2-222-2-2-2-20000-222000022-2-20000022−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-222-2-2-2-20000-222000022-2-200000−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-222-2-2-2-20000-2220000-2-2220000022−2−2−2−222−2−22222−2−200000000000000
χ302222-2-222-2-2-2-20000-2220000-2-22200000−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-222222222-22-2-222-200000000-20000000000000000002-2-2200000000
χ322222-2-2-2-222222222-22-2-222-200000000-2000000000000000000-222-200000000
χ332222-2-2-2-22222-2-2-2-2-22-22-2-22000022-2-220000000000000000-22000000000000
χ342222-2-2-2-22222-2-2-2-2-22-22-2-220000-2-222200000000000000002-2000000000000
χ352222-2-2-2-2-2-22222222-22-2-2-2-22-22-2000020000000000000000000000-22000000
χ362222-2-2-2-2-2-22222222-22-2-2-2-2-22-220000200000000000000000000002-2000000
χ3722-2-22-22-200-2222-2-2000-200200002i−2i2i−2i02−22−22−22−20000000000000000i2−i2i2−i200
χ3822-2-22-22-200-2222-2-2000-200200002i−2i2i−2i0−22−22−22−220000000000000000−i2i2−i2i200
χ3922-2-22-22-200-2222-2-2000-20020000−2i2i−2i2i02−22−22−22−20000000000000000−i2i2−i2i200
χ4022-2-22-22-200-2222-2-2000-20020000−2i2i−2i2i0−22−22−22−220000000000000000i2−i2i2−i200
χ4122-2-2-22-2200-22-2-222000-200200002i−2i−2i2i02−22−2−22−220000000000000000i2−i2−i2i200
χ4222-2-2-22-2200-22-2-222000-200200002i−2i−2i2i0−22−222−22−20000000000000000−i2i2i2−i200
χ4322-2-2-22-2200-22-2-222000-20020000−2i2i2i−2i02−22−2−22−220000000000000000−i2i2i2−i200
χ4422-2-2-22-2200-22-2-222000-20020000−2i2i2i−2i0−22−222−22−20000000000000000i2−i2−i2i200
χ45444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000
χ464444-4-44444-4-400004-4-40000000000000000000000000000000000000000000
χ4744-4-44-44-400-44-4-444000400-4000000000000000000000000000000000000000
χ4844-4-44-4-44004-4000000000000000000002-2-222-2-220000000000000000000000
χ4944-4-44-4-44004-400000000000000000000-222-2-222-20000000000000000000000
χ5044-4-4-444-4004-4000000000000000000002-2-22-222-20000000000000000000000
χ5144-4-4-444-4004-400000000000000000000-222-22-2-220000000000000000000000
χ5244-4-4-44-4400-4444-4-4000400-4000000000000000000000000000000000000000
χ534-44-400004i−4i002i2−2i22i2−2i2000022−22000000000000000000ζ+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
χ544-44-400004i−4i002i2−2i22i2−2i2000022−22000000000000000000−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
χ554-44-400004i−4i00−2i22i2−2i22i20000−2222000000000000000000ζ−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
χ564-44-400004i−4i00−2i22i2−2i22i20000−2222000000000000000000−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
χ574-44-40000−4i4i002i2−2i22i2−2i20000−2222000000000000000000ζ−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
χ584-44-40000−4i4i002i2−2i22i2−2i20000−2222000000000000000000−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
χ594-44-40000−4i4i00−2i22i2−2i22i2000022−22000000000000000000ζ+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
χ604-44-40000−4i4i00−2i22i2−2i22i2000022−22000000000000000000−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
χ618-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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