Finite Group Databasebeta

← Group #489342

Character table — Group #489342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122244444444888824488882444444481616161616161616161616161616161622444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-11111-1111111111-1-1-1-1-1-1-1-11-1-1-11-1-1-11111-1-1
χ611111111111111111111111-1-1-11111-11-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1111-11-1-11111-1-1
χ91111-1-1-1-1-1-111-1-1-1-1-111111111-111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-111-111-1-11-1
χ101111-1-1-1-1-1-111-1-1-1-1-111111111-111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-111-1-1-111-11
χ111111-1-1-1-1-1-111-1-1-1-1-111111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-111-11-1-1-111-11
χ121111-1-1-1-1-1-111-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-111-11-111-1-11-1
χ131111-1-1-1-1-1-111-1-1-1-1-1111111-1-1111-1-11-11111-1-1-1-1-1-1-1-1111111-11-1-1-1111-1-1-11
χ141111-1-1-1-1-1-111-1-1-1-1-1111111-1-1111-1-11-1-1-1-1-111111111-1-1-1-111-11-1-1-11-1-1111-1
χ151111-1-1-1-1-1-111-1-1-1-1-1111111-1-11-1-1111-11111-1-1-1-1-1-1-1-11111-1-11-111-11-1-1111-1
χ161111-1-1-1-1-1-111-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-111111111-1-1-1-1-1-11-111-1111-1-1-11
χ17222222222222-2-2-2-2222-2-2-2-222200002-20000000000000000000000-2-2000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-20000-2-2000000000000000000000022000000
χ1922222222-2-2-2-20000-2-2200002-2-200002022−2−222−2−222−2−222−2−200000000000000
χ2022222222-2-2-2-20000-2-2200002-2-2000020−2−222−2−222−2−222−2−22200000000000000
χ2122222222-2-2-2-20000-2-220000-2220000-2022−2−222−2−2−2−222−2−22200000000000000
χ2222222222-2-2-2-20000-2-220000-2220000-20−2−222−2−22222−2−222−2−200000000000000
χ23222222-2-222222222-2-2-222-2-200022220-20000000000000000-2000-2000000000
χ24222222-2-222222222-2-2-222-2-2000-2-2-2-20-2000000000000000020002000000000
χ25222222-2-22222-2-2-2-2-2-2-2-2-2220000000020000000000000000022-20-200000000
χ26222222-2-22222-2-2-2-2-2-2-2-2-22200000000200000000000000000-2-220200000000
χ272222-2-222-2-22222222-2-2-2-22200000000-2000000000000000002-2-20200000000
χ282222-2-222-2-22222222-2-2-2-22200000000-200000000000000000-2220-200000000
χ292222-2-222-2-222-2-2-2-22-2-222-2-200022-2-2020000000000000000-20002000000000
χ302222-2-222-2-222-2-2-2-22-2-222-2-2000-2-2220200000000000000002000-2000000000
χ312222-2-2-2-222-2-200002-2200002-220000-2022−2−2−2−22222−2−2−2−22200000000000000
χ322222-2-2-2-222-2-200002-2200002-220000-20−2−22222−2−2−2−22222−2−200000000000000
χ332222-2-2-2-222-2-200002-220000-22-200002022−2−2−2−222−2−22222−2−200000000000000
χ342222-2-2-2-222-2-200002-220000-22-2000020−2−22222−2−222−2−2−2−22200000000000000
χ352222-2-2-2-2-2-2222222-222-2-2-2-222-20000-220000000000000000000000-22000000
χ362222-2-2-2-2-2-2222222-222-2-2-2-2-2-2200002200000000000000000000002-2000000
χ3722-2-22i−2i002i−2i2-22i2i−2i−2i0002-2000002i−2i2-200i2−i2i2−i22−22−200000000000000002−2i2−i200
χ3822-2-22i−2i002i−2i2-22i2i−2i−2i0002-2000002i−2i2-200−i2i2−i2i2−22−220000000000000000−22−i2i200
χ3922-2-22i−2i002i−2i2-22i2i−2i−2i0002-200000−2i2i-2200i2−i2i2−i22−22−20000000000000000−22−i2i200
χ4022-2-22i−2i002i−2i2-22i2i−2i−2i0002-200000−2i2i-2200−i2i2−i2i2−22−2200000000000000002−2i2−i200
χ4122-2-2−2i2i00−2i2i2-2−2i−2i2i2i0002-2000002i−2i-2200i2−i2i2−i2−22−2200000000000000002−2−i2i200
χ4222-2-2−2i2i00−2i2i2-2−2i−2i2i2i0002-2000002i−2i-2200−i2i2−i2i22−22−20000000000000000−22i2−i200
χ4322-2-2−2i2i00−2i2i2-2−2i−2i2i2i0002-200000−2i2i2-200i2−i2i2−i2−22−220000000000000000−22i2−i200
χ4422-2-2−2i2i00−2i2i2-2−2i−2i2i2i0002-200000−2i2i2-200−i2i2−i2i22−22−200000000000000002−2−i2i200
χ45444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000000000
χ464444-4-44444-4-40000-44-40000000000000000000000000000000000000000000
χ4744-4-44i−4i004i−4i4-4−4i−4i4i4i000-4400000000000000000000000000000000000000000
χ4844-4-44i−4i00−4i4i-44000000000000000000002i−2i−2i2i2-2-220000000000000000000000
χ4944-4-44i−4i00−4i4i-4400000000000000000000−2i2i2i−2i-222-20000000000000000000000
χ5044-4-4−4i4i004i−4i-44000000000000000000002i−2i−2i2i-222-20000000000000000000000
χ5144-4-4−4i4i004i−4i-4400000000000000000000−2i2i2i−2i2-2-220000000000000000000000
χ5244-4-4−4i4i00−4i4i4-44i4i−4i−4i000-4400000000000000000000000000000000000000000
χ534-44-4004i−4i00002i2−2i22i2−2i20000022−2200000000000000000ζ+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
χ544-44-4004i−4i00002i2−2i22i2−2i20000022−2200000000000000000−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
χ554-44-4004i−4i0000−2i22i2−2i22i200000−222200000000000000000ζ−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
χ564-44-4004i−4i0000−2i22i2−2i22i200000−222200000000000000000−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
χ574-44-400−4i4i00002i2−2i22i2−2i200000−222200000000000000000ζ−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
χ584-44-400−4i4i00002i2−2i22i2−2i200000−222200000000000000000−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
χ594-44-400−4i4i0000−2i22i2−2i22i20000022−2200000000000000000ζ+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
χ604-44-400−4i4i0000−2i22i2−2i22i20000022−2200000000000000000−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
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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