Finite Group Databasebeta

← Group #489309

Character table — Group #489309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122244444444888824488882444444481616161616161616161616161616161622444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-11-1-111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-111-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ611111111111111111111111-1-1-111-1111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ91111-1-1-1-111111111-1-11-1-1111-1111-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-11-111-1-11-1
χ101111-1-1-1-111111111-1-11-1-1111-1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-11-1-1-111-11
χ111111-1-1-1-111111111-1-11-1-1111-11-1-1-111-11111-1-1-1-11111-1-1-1-1-1-11-1111-1-1-111-11
χ121111-1-1-1-111111111-1-11-1-1111-11-1-1-111-1-1-1-1-11111-1-1-1-11111-1-11-1111-111-1-11-1
χ131111-1-1-1-111111111-1-11-1-111-11-1111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-11-1-1111-1
χ141111-1-1-1-111111111-1-11-1-111-11-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1111-1-1-11
χ151111-1-1-1-111111111-1-11-1-111-11-1-1-1111-11111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-1-11
χ161111-1-1-1-111111111-1-11-1-111-11-1-1-1111-1-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-1111-1
χ17222222222222-2-2-2-2222-2-2-2-222200200-20000000000000000000000-2-2000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-200-200-2000000000000000000000022000000
χ1922222222-2-2222222-2-2-222-2-200022022-2000000000000000000-2-20000000000
χ2022222222-2-2222222-2-2-222-2-2000-2-20-2-2-2000000000000000000220000000000
χ2122222222-2-222-2-2-2-2-2-2-2-2-22200000000200000000000000002-2002-200000000
χ2222222222-2-222-2-2-2-2-2-2-2-2-2220000000020000000000000000-2200-2200000000
χ23222222-2-222-2-200002-2-200002-2-200200022−2−222−2−222−2−222−2−200000000000000
χ24222222-2-222-2-200002-2-200002-2-2002000−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-222-2-200002-2-20000-22200-200022−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-222-2-200002-2-20000-22200-2000−2−222−2−22222−2−222−2−200000000000000
χ272222-2-22222-2-20000-22-2000022-200-200022−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-22222-2-20000-22-2000022-200-2000−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-22222-2-20000-22-20000-2-2200200022−2−2−2−222−2−22222−2−200000000000000
χ302222-2-22222-2-20000-22-20000-2-22002000−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-22222-2-2-2-2-2-2222-2-22-2200-20020000000000000000000000-22000000
χ322222-2-2-2-22222-2-2-2-2-2-2222-2-2-22-200200200000000000000000000002-2000000
χ332222-2-2-2-2-2-222222222-2-2-2-2-2000220-2-220000000000000000002-20000000000
χ342222-2-2-2-2-2-222222222-2-2-2-2-2000-2-20222000000000000000000-220000000000
χ352222-2-2-2-2-2-222-2-2-2-222-2222200000000-200000000000000002-200-2200000000
χ362222-2-2-2-2-2-222-2-2-2-222-2222200000000-20000000000000000-22002-200000000
χ372-22-22i−2i2i−2i002-222-2-20002i−2i000002-202i−2i0000000002−22−2i2−i2i2−i2000000002−2i2−i200
χ382-22-22i−2i2i−2i002-222-2-20002i−2i000002-202i−2i000000000−22−22−i2i2−i2i200000000−22−i2i200
χ392-22-22i−2i2i−2i002-222-2-20002i−2i00000-220−2i2i0000000002−22−2i2−i2i2−i200000000−22−i2i200
χ402-22-22i−2i2i−2i002-222-2-20002i−2i00000-220−2i2i000000000−22−22−i2i2−i2i2000000002−2i2−i200
χ412-22-2−2i2i−2i2i002-222-2-2000−2i2i000002-20−2i2i0000000002−22−2−i2i2−i2i2000000002−2−i2i200
χ422-22-2−2i2i−2i2i002-222-2-2000−2i2i000002-20−2i2i000000000−22−22i2−i2i2−i200000000−22i2−i200
χ432-22-2−2i2i−2i2i002-222-2-2000−2i2i00000-2202i−2i0000000002−22−2−i2i2−i2i200000000−22i2−i200
χ442-22-2−2i2i−2i2i002-222-2-2000−2i2i00000-2202i−2i000000000−22−22i2−i2i2−i2000000002−2−i2i200
χ45444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000000
χ464444-4-444-4-4-4-400004-440000000000000000000000000000000000000000000
χ4744-4-400004-40022−2222−220000022−2200000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000
χ4844-4-400004-40022−2222−220000022−220000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000
χ4944-4-400004-400−2222−222200000−222200000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000
χ5044-4-400004-400−2222−222200000−22220000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000
χ5144-4-40000-440022−2222−2200000−22220000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ5244-4-40000-440022−2222−2200000−2222000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ5344-4-40000-4400−2222−22220000022−220000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ5444-4-40000-4400−2222−22220000022−22000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ554-44-44i−4i4i−4i004-4-4-444000−4i4i00000000000000000000000000000000000000000
χ564-44-44i−4i−4i4i00-4400000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ574-44-44i−4i−4i4i00-440000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ584-44-4−4i4i4i−4i00-4400000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ594-44-4−4i4i4i−4i00-440000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ604-44-4−4i4i−4i4i004-4-4-4440004i−4i00000000000000000000000000000000000000000
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.