Finite Group Databasebeta

← Group #492821

Character table — Group #492821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444444444444444448888888816161616161616161616161632323232
order1222444488888888488888888161616161616161616161616161616164444444424888888161616164444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-11111-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1111111-1-1
χ911111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-111-1-11-11-1
χ1011111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-111-11-11
χ1111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-11-11
χ1211111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-1111-11-1
χ1311111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-1-1111-1-1-1111-1-11
χ1411111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1-111-1111-1-1-111-1
χ1511111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1111-1-11-1-1-111-111-1
χ1611111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1111-1-1-1111-1-11-1-11
χ17222222222222-2-2-2-2222-2-2-2-2-2-2000000000000000000002222000000-2-200000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-200000000000000000000-2-2-2-20000002200000000
χ1922222222-2-2-2-2-2-2-2-22-2-22222-2-20000000000000000000022-2-2000000-2200000000
χ2022222222-2-2-2-2-2-2-2-22-2-22222-2-200000000000000000000-2-2220000002-200000000
χ2122222-2-2200002222-2000000-2-22222-2-2-2-20000000022220000-2-200000000000000
χ2222222-2-2200002222-2000000-2-22222-2-2-2-200000000-2-2-2-200002200000000000000
χ2322222-2-2200002222-2000000-2-2-2-2-2-222220000000022-2-20000-2200000000000000
χ2422222-2-2200002222-2000000-2-2-2-2-2-2222200000000-2-22200002-200000000000000
χ252222-222-222220000-2-2-200000022−2−222−2−22222−2−2−2−200002-22-2000000002−22−20000
χ262222-222-222220000-2-2-200000022−2−222−2−22222−2−2−2−20000-22-2200000000−22−220000
χ272222-222-222220000-2-2-2000000−2−222−2−222−2−2−2−2222200002-22-200000000−22−220000
χ282222-222-222220000-2-2-2000000−2−222−2−222−2−2−2−222220000-22-22000000002−22−20000
χ292222-222-2-2-2-2-20000-22200000022−2−222−2−2−2−2−2−2222200002-2-22000000002−2−220000
χ302222-222-2-2-2-2-20000-22200000022−2−222−2−2−2−2−2−222220000-222-200000000−222−20000
χ312222-222-2-2-2-2-20000-222000000−2−222−2−2222222−2−2−2−200002-2-2200000000−222−20000
χ322222-222-2-2-2-2-20000-222000000−2−222−2−2222222−2−2−2−20000-222-2000000002−2−220000
χ332-2-22200-222−2−222-2-202−222−2−2002-22-2000022−2−222−2−22i−2i2i−2i000000i2−i2i2−i20000000000
χ342-2-22200-222−2−222-2-202−222−2−2002-22-2000022−2−222−2−2−2i2i−2i2i000000−i2i2−i2i20000000000
χ352-2-22200-222−2−222-2-202−222−2−200-22-220000−2−222−2−2222i−2i−2i2i000000i2−i2−i2i20000000000
χ362-2-22200-222−2−222-2-202−222−2−200-22-220000−2−222−2−222−2i2i2i−2i000000−i2i2i2−i20000000000
χ372-2-22200-2−2−22222-2-20−22−2−222002-22-20000−2−222−2−2222i−2i2i−2i000000−i2i2−i2i20000000000
χ382-2-22200-2−2−22222-2-20−22−2−222002-22-20000−2−222−2−222−2i2i−2i2i000000i2−i2i2−i20000000000
χ392-2-22200-2−2−22222-2-20−22−2−22200-22-22000022−2−222−2−22i−2i−2i2i000000−i2i2i2−i20000000000
χ402-2-22200-2−2−22222-2-20−22−2−22200-22-22000022−2−222−2−2−2i2i2i−2i000000i2−i2−i2i20000000000
χ4144444-4-440000-4-4-4-4-4000000440000000000000000000000000000000000000000
χ424444-4-4-4-4000000004000000002222−22−22−22−22222200000000000000000000000000000000
χ434444-4-4-4-400000000400000000−22−2222222222−22−2200000000000000000000000000000000
χ4444-4-4000022−2222−2222−2222−220002-22-20000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7ζ−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+ζ7000000000000000000000000
χ4544-4-4000022−2222−2222−2222−220002-22-2000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−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−ζ7000000000000000000000000
χ4644-4-4000022−2222−22−2222−2222000-22-220000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5ζ+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−ζ7000000000000000000000000
χ4744-4-4000022−2222−22−2222−2222000-22-22000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−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+ζ7000000000000000000000000
χ4844-4-40000−2222−222222−2222−22000-22-220000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−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−ζ7000000000000000000000000
χ4944-4-40000−2222−222222−2222−22000-22-22000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7ζ−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+ζ7000000000000000000000000
χ5044-4-40000−2222−2222−2222−22220002-22-20000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−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+ζ7000000000000000000000000
χ5144-4-40000−2222−2222−2222−22220002-22-2000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5ζ+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−ζ7000000000000000000000000
χ524-44-404-40000022−22−2222000000022−22000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ534-44-404-40000022−22−2222000000022−2200000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ544-44-404-400000−222222−220000000−2222000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ554-44-404-400000−222222−220000000−222200000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ564-44-40-4404-4-4422−22−222200022−22−2222−22220000000000000000000000000000000000000000
χ574-44-40-4404-4-44−222222−22000−222222−2222−220000000000000000000000000000000000000000
χ584-44-40-440-444-422−22−2222000−222222−22−22220000000000000000000000000000000000000000
χ594-44-40-440-444-4−222222−2200022−22−222222−220000000000000000000000000000000000000000
χ604-4-44400-42222−22−22-4-444022−22−22−222222000000000000000000000000000000000000000000
χ614-4-44400-4−22−222222-4-4440−22222222−22−22000000000000000000000000000000000000000000
χ624-4-44-40042222−22−2200000−222200000022−22−2222000022-2-2-2-222000000000000000000000000
χ634-4-44-40042222−22−2200000−2222000000−222222−220000-2-22222-2-2000000000000000000000000
χ644-4-44-4004−22−2222220000022−2200000022−22−22220000-2-22222-2-2000000000000000000000000
χ654-4-44-4004−22−2222220000022−22000000−222222−22000022-2-2-2-222000000000000000000000000

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