Finite Group Databasebeta

← Group #489273

Character table — Group #489273

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222444444444488882488888816161616161616161616161616161616222444444444448888881616161624
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-1-1-1-1-111111111-11-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-11-1-11-111-1-111-1-11-111-1-11-1
χ101111-1-1-1-1-1-111111111-11-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-11111-1-1-11-1-111-11
χ111111-1-1-1-1-1-111111111-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-1111-111-1-1-11
χ121111-1-1-1-1-1-111111111-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-111-1111-1-1-1-111-11-1-1111-1
χ131111-1-1-1-1-1-111111111-11-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-11-1-11-111-1-1-1-1111-1-1-111-11
χ141111-1-1-1-1-1-111111111-11-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-111-1-111-1111-1-11-1
χ151111-1-1-1-1-1-111111111-11-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-1-11111-1-11-1-1-1111-1
χ161111-1-1-1-1-1-111111111-11-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111-111-1111-1-111-1-1-1111-1-1-11
χ1722222222222222-2-2-2-222-2-2-2-2-2-20000000000000000002002220000000000-2-2000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000-200-2-2-2000000000022000000
χ1922222222-2-222-2-20000-2-20000002222−2−2−2−22222−2−2−2−200200-22-20000000000002−22−200
χ2022222222-2-222-2-20000-2-20000002222−2−2−2−22222−2−2−2−200-2002-22000000000000−22−2200
χ2122222222-2-222-2-20000-2-2000000−2−2−2−22222−2−2−2−2222200200-22-2000000000000−22−2200
χ2222222222-2-222-2-20000-2-2000000−2−2−2−22222−2−2−2−2222200-2002-220000000000002−22−200
χ23222222-2-222-2-2222222-2-222-2-2-2-2000000000000000022022000-2-20000000000000000
χ24222222-2-222-2-2222222-2-222-2-2-2-20000000000000000-2-20-2-2000220000000000000000
χ25222222-2-222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000002-22-2000000000000
χ26222222-2-222-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000-22-22000000000000
χ272222-2-222-2-2-2-22222222-2-2-222-2-20000000000000000220-2-2000-220000000000000000
χ282222-2-222-2-2-2-22222222-2-2-222-2-20000000000000000-2-20220002-20000000000000000
χ292222-2-222-2-2-2-222-2-2-2-22-222-2-222000000000000000000000000002-2-22000000000000
χ302222-2-222-2-2-2-222-2-2-2-22-222-2-22200000000000000000000000000-222-2000000000000
χ312222-2-2-2-22222-2-200002-20000002222−2−2−2−2−2−2−2−2222200200-2-220000000000002−2−2200
χ322222-2-2-2-22222-2-200002-20000002222−2−2−2−2−2−2−2−2222200-20022-2000000000000−222−200
χ332222-2-2-2-22222-2-200002-2000000−2−2−2−222222222−2−2−2−200200-2-22000000000000−222−200
χ342222-2-2-2-22222-2-200002-2000000−2−2−2−222222222−2−2−2−200-20022-20000000000002−2−2200
χ352222-2-2-2-2-2-22222-2-2-2-2-222222-2-20000000000000000002002-2-20000000000-22000000
χ362222-2-2-2-2-2-22222-2-2-2-2-222222-2-2000000000000000000-200-22200000000002-2000000
χ3722-2-22i−2i002i−2i002-222-2-2002i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i22-202i−2i0000000002−2i2−i200000000
χ3822-2-22i−2i002i−2i002-222-2-2002i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2-220−2i2i000000000−22−i2i200000000
χ3922-2-22i−2i002i−2i002-222-2-2002i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i22-202i−2i000000000−22−i2i200000000
χ4022-2-22i−2i002i−2i002-222-2-2002i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i2-220−2i2i0000000002−2i2−i200000000
χ4122-2-2−2i2i00−2i2i002-222-2-200−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i22-20−2i2i0000000002−2−i2i200000000
χ4222-2-2−2i2i00−2i2i002-222-2-200−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2-2202i−2i000000000−22i2−i200000000
χ4322-2-2−2i2i00−2i2i002-222-2-200−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i22-20−2i2i000000000−22i2−i200000000
χ4422-2-2−2i2i00−2i2i002-222-2-200−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i2-2202i−2i0000000002−2−i2i200000000
χ45444444-4-4-4-4-4-4-4-4000044000000000000000000000000000000000000000000000000
χ464444-4-44444-4-4-4-40000-44000000000000000000000000000000000000000000000000
χ4744-4-44i−4i004i−4i004-4-4-44400−4i4i0000000000000000000000000000000000000000000000
χ4844-4-44i−4i00−4i4i00-4400000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ4944-4-44i−4i00−4i4i00-44000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ5044-4-4−4i4i004i−4i00-4400000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ5144-4-4−4i4i004i−4i00-44000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ5244-4-4−4i4i00−4i4i004-4-4-444004i−4i0000000000000000000000000000000000000000000000
χ534-44-4004i−4i00000022−2222−2200002i2−2i200ζ+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−ζ7ζ+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+ζ700000000000000000000000000
χ544-44-4004i−4i00000022−2222−2200002i2−2i200−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+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+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000
χ554-44-4004i−4i000000−2222−22220000−2i22i200ζ−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+ζ7−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+ζ700000000000000000000000000
χ564-44-4004i−4i000000−2222−22220000−2i22i200−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−ζ7ζ−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−ζ700000000000000000000000000
χ574-44-400−4i4i00000022−2222−220000−2i22i200ζ+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−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+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000
χ584-44-400−4i4i00000022−2222−220000−2i22i200−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+ζ7ζ+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+ζ700000000000000000000000000
χ594-44-400−4i4i000000−2222−222200002i2−2i200ζ−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+ζ7ζ−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−ζ700000000000000000000000000
χ604-44-400−4i4i000000−2222−222200002i2−2i200−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−ζ7−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+ζ700000000000000000000000000
χ614-4-440000004-40022−22−222200000022−22000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ624-4-440000004-40022−22−222200000022−2200000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ634-4-440000004-400−222222−22000000−2222000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
χ644-4-440000004-400−222222−22000000−222200000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ654-4-44000000-440022−22−2222000000−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ70000000000000000000000000000000000
χ664-4-44000000-440022−22−2222000000−2222−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ70000000000000000000000000000000000
χ674-4-44000000-4400−222222−2200000022−222ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000000000
χ684-4-44000000-4400−222222−2200000022−22−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000000000

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