Finite Group Databasebeta

← Group #318575

Character table — Group #318575

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244444444448888888888882222444488888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11-11-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-11-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111-11-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-11-1111-1-11-1-11
χ1722222222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000002i−2i2i−2i0000
χ1822222222-2-222-2-2-2-22222-2-2-2-2000000000000000000000000000000−2i2i−2i2i0000
χ1922222222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000002i−2i−2i2i0000
χ2022222222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000−2i2i2i−2i0000
χ21222222-2-222-2-222-2-20000000022222222-2-2-2-2-2-2000000000000000000000000
χ22222222-2-222-2-222-2-2000000002222-2-2-2-22222-2-2000000000000000000000000
χ23222222-2-222-2-222-2-200000000-2-2-2-222-2-2-2-22222000000000000000000000000
χ24222222-2-222-2-222-2-200000000-2-2-2-2-2-22222-2-222000000000000000000000000
χ252222-2-222-22-2-22-22-20000000022-2-2000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000
χ262222-2-222-22-2-22-22-20000000022-2-2000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000
χ272222-2-222-22-2-22-22-200000000-2-22200000000-222i2i−2i−2i−2i−2i2i2i0000000000000000
χ282222-2-222-22-2-22-22-200000000-2-22200000000-22−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-22-222-222-222-2-222-2-20000000000000000000000000022-2-200000000
χ302222-2-2-2-22-222-222-222-2-222-2-200000000000000000000000000-2-22200000000
χ312222-2-2-2-22-222-222-2-2-222-2-222000000000000000000000000002-2-2200000000
χ322222-2-2-2-22-222-222-2-2-222-2-22200000000000000000000000000-222-200000000
χ332222-2-2-2-2-22222-2-2222-2-2-2-22222-2-200000000-220000000022-2-2000000000000
χ342222-2-2-2-2-22222-2-2222-2-2-2-222-2-222000000002-200000000-2-222000000000000
χ352222-2-2-2-2-22222-2-22-2-22222-2-222-2-200000000-2200000000-2-222000000000000
χ362222-2-2-2-2-22222-2-22-2-22222-2-2-2-222000000002-20000000022-2-2000000000000
χ372-22-22-2002-2002-2002−22−22−22−22-22-200002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ382-22-22-2002-2002-2002−22−22−22−22-22-20000−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ392-22-22-2002-2002-2002−22−22−22−2-22-2200002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ402-22-22-2002-2002-2002−22−22−22−2-22-220000−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ412-22-22-2002-2002-200−22−22−22−222-22-200002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ422-22-22-2002-2002-200−22−22−22−222-22-20000−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ432-22-22-2002-2002-200−22−22−22−22-22-2200002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ442-22-22-2002-2002-200−22−22−22−22-22-220000−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ452-22-2-2200-2-20022002−2−22−222−22-2-222-22-20000002−2−222−2−222−2−22000000000000
χ462-22-2-2200-2-20022002−2−22−222−22-2-22-22-22000000−222−2−222−22−2−22000000000000
χ472-22-2-2200-2-20022002−2−22−222−2-222-22-2-220000002−2−22−222−2−222−2000000000000
χ482-22-2-2200-2-20022002−2−22−222−2-222-2-222-2000000−222−22−2−22−222−2000000000000
χ492-22-2-2200-2-2002200−222−22−2−222-2-222-22-2000000−222−2−222−2−222−2000000000000
χ502-22-2-2200-2-2002200−222−22−2−222-2-22-22-220000002−2−222−2−22−222−2000000000000
χ512-22-2-2200-2-2002200−222−22−2−22-222-22-2-22000000−222−22−2−222−2−22000000000000
χ522-22-2-2200-2-2002200−222−22−2−22-222-2-222-20000002−2−22−222−22−2−22000000000000
χ53444444-4-4-4-4-4-4-4-4440000000000000000000000000000000000000000000000
χ544444-4-4444-4-4-4-44-440000000000000000000000000000000000000000000000
χ554-44-44-400-4400-440022−2222−22−2222−222200000000000000000000000000000000000000
χ564-44-44-400-4400-4400−2222−222222−2222−2200000000000000000000000000000000000000
χ574-44-4-44004400-4-40022−22−222222−22−222200000000000000000000000000000000000000
χ584-44-4-44004400-4-400−222222−22−222222−2200000000000000000000000000000000000000
χ5988-8-8008i−8i000000000000000000000000000000000000000000000000000000
χ6088-8-800−8i8i000000000000000000000000000000000000000000000000000000
χ618-8-880000008-800000000000000000000000000000000000000000000000000
χ628-8-88000000-8800000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).