Finite Group Databasebeta

← Group #489272

Character table — Group #489272

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222224444444488884488888816161616161616161616161616161616244444444444448888881616161624
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1
χ91111-1-11-1-1-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-1111-1-1-11-111-1-111-1-11-1
χ101111-1-11-1-1-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-11111-1-1-11111-1-1-11
χ111111-1-11-1-1-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-11-111-1111-1-1-1-111-11
χ121111-1-11-1-1-1-111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-11111-11-1-1-11-1-111-1-1111-1
χ131111-1-11-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-111-1-1111-1-1-11-1-1-111-1-111-11
χ141111-1-11-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-1-11111-111-1-1-1-1111-1
χ151111-1-11-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-11-111-11-1-11111-1-11-1
χ161111-1-11-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-11111-11-1-1-1111-1-111-1-1-11
χ1722222222222222-2-2-2-222-2-2-2-2-2-2000000000000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-20000000000000000-2-2-2-20000000000220000000000
χ19222222222-2-2-2-220000-2-20000002222−2−2−2−22222−2−2−2−22-2-2200000000000000002−22−200
χ20222222222-2-2-2-220000-2-20000002222−2−2−2−22222−2−2−2−2-222-20000000000000000−22−2200
χ21222222222-2-2-2-220000-2-2000000−2−2−2−22222−2−2−2−222222-2-220000000000000000−22−2200
χ22222222222-2-2-2-220000-2-2000000−2−2−2−22222−2−2−2−22222-222-200000000000000002−22−200
χ23222222-2-2-2-2-222-22222-2222-2-2-2-20000000000000000000022-2-200-2200000000000000
χ24222222-2-2-2-2-222-22222-2222-2-2-2-200000000000000000000-2-222002-200000000000000
χ25222222-2-2-2-2-222-2-2-2-2-2-22-2-222220000000000000000000000002-2002-2000000000000
χ26222222-2-2-2-2-222-2-2-2-2-2-22-2-22222000000000000000000000000-2200-22000000000000
χ272222-2-22-2-222-2-220000-220000002222−2−2−2−2−2−2−2−2222222-2-200000000000000002−2−2200
χ282222-2-22-2-222-2-220000-220000002222−2−2−2−2−2−2−2−22222-2-2220000000000000000−222−200
χ292222-2-22-2-222-2-220000-22000000−2−2−2−222222222−2−2−2−222-2-20000000000000000−222−200
χ302222-2-22-2-222-2-220000-22000000−2−2−2−222222222−2−2−2−2-2-22200000000000000002−2−2200
χ312222-2-22-2-2-2-2222-2-2-2-22-22222-2-200000000000000002-22-20000000000-220000000000
χ322222-2-22-2-2-2-2222-2-2-2-22-22222-2-20000000000000000-22-2200000000002-20000000000
χ332222-2-2-2222222-22222-2-2-2-222-2-200000000000000000000222200-2-200000000000000
χ342222-2-2-2222222-22222-2-2-2-222-2-200000000000000000000-2-2-2-2002200000000000000
χ352222-2-2-2222222-2-2-2-2-2-2-222-2-2220000000000000000000000002-200-22000000000000
χ362222-2-2-2222222-2-2-2-2-2-2-222-2-222000000000000000000000000-22002-2000000000000
χ372-22-20002i−2i2i−2i2-2022-2-200002i−2i00i2i2−i2−i2i2i2−i2−i222−2−222−2−200002i−2i2-2000000002−2i2−i2000000
χ382-22-20002i−2i2i−2i2-2022-2-200002i−2i00i2i2−i2−i2i2i2−i2−i222−2−222−2−20000−2i2i-2200000000−22−i2i2000000
χ392-22-20002i−2i2i−2i2-2022-2-200002i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−2−22200002i−2i2-200000000−22−i2i2000000
χ402-22-20002i−2i2i−2i2-2022-2-200002i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000−2i2i-22000000002−2i2−i2000000
χ412-22-2000−2i2i−2i2i2-2022-2-20000−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−2−22200002i−2i-22000000002−2−i2i2000000
χ422-22-2000−2i2i−2i2i2-2022-2-20000−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000−2i2i2-200000000−22i2−i2000000
χ432-22-2000−2i2i−2i2i2-2022-2-20000−2i2i00−i2−i2i2i2−i2−i2i2i222−2−222−2−200002i−2i-2200000000−22i2−i2000000
χ442-22-2000−2i2i−2i2i2-2022-2-20000−2i2i00−i2−i2i2i2−i2−i2i2i222−2−222−2−20000−2i2i2-2000000002−2−i2i2000000
χ45444444-4-4-444-4-4-400004-4000000000000000000000000000000000000000000000000
χ464444-4-4-444-4-4-4-4-4000044000000000000000000000000000000000000000000000000
χ4744-4-4004000000-422−2222−2200000022−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000
χ4844-4-4004000000-422−2222−2200000022−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000
χ4944-4-4004000000-4−2222−2222000000−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000
χ5044-4-4004000000-4−2222−2222000000−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000
χ5144-4-400-4000000422−2222−22000000−2222000000002ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ5244-4-400-4000000422−2222−22000000−222200000000−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ5344-4-400-40000004−2222−222200000022−22000000002ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ5444-4-400-40000004−2222−222200000022−2200000000−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
χ554-44-40004i−4i4i−4i4-40-4-4440000−4i4i00000000000000000000000000000000000000000000
χ564-44-40004i−4i−4i4i-4400000000000002i2i−2i−2i−2i−2i2i2i22-2-2-2-22200000000000000000000000000
χ574-44-40004i−4i−4i4i-440000000000000−2i−2i2i2i2i2i−2i−2i-2-22222-2-200000000000000000000000000
χ584-44-4000−4i4i4i−4i-4400000000000002i2i−2i−2i−2i−2i2i2i-2-22222-2-200000000000000000000000000
χ594-44-4000−4i4i4i−4i-440000000000000−2i−2i2i2i2i2i−2i−2i22-2-2-2-22200000000000000000000000000
χ604-44-4000−4i4i−4i4i4-40-4-44400004i−4i00000000000000000000000000000000000000000000
χ614-4-444-40000000022−22−22220022−220000ζ+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+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000000000
χ624-4-444-40000000022−22−22220022−220000−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−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000000000
χ634-4-444-400000000−222222−2200−22220000ζ−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+ζ7ζ−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+ζ700000000000000000000000000
χ644-4-444-400000000−222222−2200−22220000−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−ζ7−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−ζ700000000000000000000000000
χ654-4-44-440000000022−22−222200−22220000ζ+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−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+ζ700000000000000000000000000
χ664-4-44-440000000022−22−222200−22220000−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+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−ζ700000000000000000000000000
χ674-4-44-4400000000−222222−220022−220000ζ−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+ζ7−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−ζ700000000000000000000000000
χ684-4-44-4400000000−222222−220022−220000−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−ζ7ζ−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+ζ700000000000000000000000000

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