Finite Group Databasebeta

← Group #492648

Character table — Group #492648

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444488888888888888888888816161616161616161632323232
order122244448888224888888161616164444444888816161616161616161616248888816162444
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-11-1-111111111111111-1-11-1-1-1-111-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1
χ4111111111111111111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11-1-11
χ5111111111111111-1-1-1-1111111-1111-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-11
χ6111111111111111-1-1-1-1111111-11-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11111-1-11-11-1
χ7111111111111111-1-1-1-111-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-11111-11-1-1-1111111-1-1
χ8111111111111111-1-1-1-111-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111
χ9111111111111-1-111111111111-1-111-111-1-11111-1-1-1-1111111-11111-1-1-1-1-1-1
χ10111111111111-1-111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11111
χ11111111111111-1-11111111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-11-111-1-1111-1-11
χ12111111111111-1-11111111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11-1-1-1-11111-111-1
χ13111111111111-1-11-1-1-1-11111111-111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-11-1
χ14111111111111-1-11-1-1-1-11111111-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-11-11
χ15111111111111-1-11-1-1-1-111-1-1-1-11-1111-1-1-1-1-1-1-1-111111111-111-1-111-1-1-1-111
χ16111111111111-1-11-1-1-1-111-1-1-1-11-1-1-1111-1-1-1-1-1-1111111111-1111-1-1-1-111-1-1
χ1722222222-2-2-2-22222222-2-200002200200-2-2-2-2000000000000-20000000000
χ1822222222-2-2-2-2222-2-2-2-2-2-20000-2200-200-2-22200000000000020000000000
χ1922222222-2-2-2-2-2-222222-2-20000-2-200-20022-2-200000000000020000000000
χ2022222222-2-2-2-2-2-22-2-2-2-2-2-200002-2002002222000000000000-20000000000
χ2122222-2-22000022-222-2-20022−2−22-200-20000002−222−2−222−2−200000002−20000
χ2222222-2-22000022-222-2-200−2−2222-200-2000000−22−2−222−2−2220000000−220000
χ2322222-2-22000022-2-2-2220022−2−2-2-20020000002−222−2−2−2−2220000000−220000
χ2422222-2-22000022-2-2-22200−2−222-2-2002000000−22−2−22222−2−200000002−20000
χ2522222-2-220000-2-2-222-2-20022−2−2-220020000002−2−2−22222−2−20000000−220000
χ2622222-2-220000-2-2-222-2-200−2−222-22002000000−2222−2−2−2−22200000002−20000
χ2722222-2-220000-2-2-2-2-2220022−2−22200-20000002−2−2−222−2−22200000002−20000
χ2822222-2-220000-2-2-2-2-22200−2−2222200-2000000−2222−2−222−2−20000000−220000
χ292222-222-2222200-20000-2-2222200220220000-2-200000000-2-200000000000
χ302222-222-2222200-20000-2-2222200-2-20-2-20000-2-2000000002200000000000
χ312222-222-2222200-20000-2-2-2-2-2-200220-2-2000022000000002-200000000000
χ322222-222-2222200-20000-2-2-2-2-2-200-2-202200002200000000-2200000000000
χ332-22-202-2022-2-2000i2−i2i2−i2002i−2i2i−2i002-202i−2i00i2−i20000002−22−2000i2−i22−2000000
χ342-22-202-2022-2-2000i2−i2i2−i2002i−2i2i−2i00-220−2i2i00i2−i20000002−22−2000−i2i2−22000000
χ352-22-202-2022-2-2000i2−i2i2−i200−2i2i−2i2i002-20−2i2i00i2−i2000000−22−22000i2−i2−22000000
χ362-22-202-2022-2-2000i2−i2i2−i200−2i2i−2i2i00-2202i−2i00i2−i2000000−22−22000−i2i22−2000000
χ372-22-202-2022-2-2000−i2i2−i2i2002i−2i2i−2i002-202i−2i00−i2i2000000−22−22000−i2i2−22000000
χ382-22-202-2022-2-2000−i2i2−i2i2002i−2i2i−2i00-220−2i2i00−i2i2000000−22−22000i2−i22−2000000
χ392-22-202-2022-2-2000−i2i2−i2i200−2i2i−2i2i002-20−2i2i00−i2i20000002−22−2000−i2i22−2000000
χ402-22-202-2022-2-2000−i2i2−i2i200−2i2i−2i2i00-2202i−2i00−i2i20000002−22−2000i2−i2−22000000
χ414444-444-4-4-4-4-400-400004400000000000000000000000000000000000000
χ424444-4-4-4-400000040000002222−22−2200000000000−2222000000000000000000000
χ434444-4-4-4-40000004000000−22−2222220000000000022−22000000000000000000000
χ444-44-404-40-4-4440002i2−2i22i2−2i2000000000000000−2i22i200000000000000000000000
χ454-44-404-40-4-444000−2i22i2−2i22i20000000000000002i2−2i200000000000000000000000
χ464-44-40-44000000002i2−2i2−2i22i2002i2−2i2−2i22i2000000000000000002-2-220000000000000
χ474-44-40-44000000002i2−2i2−2i22i200−2i22i22i2−2i200000000000000000-222-20000000000000
χ484-44-40-4400000000−2i22i22i2−2i2002i2−2i2−2i22i200000000000000000-222-20000000000000
χ494-44-40-4400000000−2i22i22i2−2i200−2i22i22i2−2i2000000000000000002-2-220000000000000
χ504-4-44400-422−2222−22000000022−22000000000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000
χ514-4-44400-422−2222−22000000022−2200000000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000
χ524-4-44400-4−2222−22220000000−2222000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000
χ534-4-44400-4−2222−22220000000−222200000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000
χ544-4-44-400422−2222−224-400000−22220000000000022−220000000000000000000000000
χ554-4-44-400422−2222−22-4400000−222200000000000−22220000000000000000000000000
χ564-4-44-4004−2222−22224-40000022−2200000000000−22220000000000000000000000000
χ574-4-44-4004−2222−2222-440000022−220000000000022−220000000000000000000000000
χ5888-8-8000042−42−424200000000000000000000000000000000000000000000000
χ5988-8-80000−424242−4200000000000000000000000000000000000000000000000

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