Finite Group Databasebeta

← Group #492658

Character table — Group #492658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444444444444444448888888816161616161616161616161632323232
order1222444488888888488888888161616161616161616161616161616162224444424888888161616164444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-111-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1111-1-11-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-111111-1-1-1-1-1-11-11-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-11111-11-11
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-111-1-1-1-1-11-11
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-11111111-11-1
χ911111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1111-1111-1-1-1-1-111-1-11-1-11
χ1011111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-111111-11-1-1-1-1-1-111-111-1
χ1111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1111111-1-1-111-1
χ1211111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-111111-1-1111-1-11
χ1311111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-11-1-1-1-111-1-1-111-1-11111-1-1
χ1411111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-11-1-1-11-11-11-1-11111-1-1-1-111
χ1511111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1111-11-11-111-1-1-1-111-1-111
χ1611111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11-11111-1-1111-1-111-1-111-1-1
χ17222222222222-2-2-2-2222-2-2-2-2-2-200000000000000000022200200-2-2000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2000000000000000000-2-2-200-20022000000000000
χ1922222222-2-2-2-2-2-2-2-22-2-22222-2-20000000000000000002-2200-200-22000000000000
χ2022222222-2-2-2-2-2-2-2-22-2-22222-2-2000000000000000000-22-2002002-2000000000000
χ2122222-2-2222220000-2-2-20000002222−2−2−2−22222−2−2−2−20022-200-2000000002−22−20000
χ2222222-2-2222220000-2-2-20000002222−2−2−2−22222−2−2−2−200-2-2200200000000−22−220000
χ2322222-2-2222220000-2-2-2000000−2−2−2−22222−2−2−2−222220022-200-200000000−22−220000
χ2422222-2-2222220000-2-2-2000000−2−2−2−22222−2−2−2−2222200-2-22002000000002−22−20000
χ2522222-2-22-2-2-2-20000-2220000002222−2−2−2−2−2−2−2−22222002-2-2002000000002−2−220000
χ2622222-2-22-2-2-2-20000-2220000002222−2−2−2−2−2−2−2−2222200-22200-200000000−222−20000
χ2722222-2-22-2-2-2-20000-222000000−2−2−2−222222222−2−2−2−2002-2-200200000000−222−20000
χ2822222-2-22-2-2-2-20000-222000000−2−2−2−222222222−2−2−2−200-22200-2000000002−2−220000
χ292222-222-200002222-2000000-2-222-2-222-2-20000000022000220-2-200000000000000
χ302222-222-200002222-2000000-2-222-2-222-2-200000000-2-2000-2-202200000000000000
χ312222-222-200002222-2000000-2-2-2-222-2-2220000000022000-2-202-200000000000000
χ322222-222-200002222-2000000-2-2-2-222-2-22200000000-2-2000220-2200000000000000
χ332-22-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i2002i−2i002i−2i0022−2−222−2−22-20002i−2i00000i2−i22−200000000
χ342-22-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i2002i−2i002i−2i0022−2−222−2−2-22000−2i2i00000−i2i2−2200000000
χ352-22-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i200−2i2i00−2i2i00−2−222−2−2222-2000−2i2i00000i2−i2−2200000000
χ362-22-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i200−2i2i00−2i2i00−2−222−2−222-220002i−2i00000−i2i22−200000000
χ372-22-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i2002i−2i002i−2i00−2−222−2−2222-20002i−2i00000−i2i2−2200000000
χ382-22-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i2002i−2i002i−2i00−2−222−2−222-22000−2i2i00000i2−i22−200000000
χ392-22-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i200−2i2i00−2i2i0022−2−222−2−22-2000−2i2i00000−i2i22−200000000
χ402-22-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i200−2i2i00−2i2i0022−2−222−2−2-220002i−2i00000i2−i2−2200000000
χ414444-444-40000-4-4-4-4-4000000440000000000000000000000000000000000000000
χ424444-4-4-4-4000000004000000002222−22−22−22−22222200000000000000000000000000000000
χ434444-4-4-4-400000000400000000−22−2222222222−22−2200000000000000000000000000000000
χ4444-4-4000022−2222−2222−2222−220002-22-200002ζ3−2ζ5−2ζ3+2ζ5002ζ−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
χ4544-4-4000022−2222−2222−2222−220002-22-20000−2ζ3+2ζ52ζ3−2ζ500−2ζ+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
χ4644-4-4000022−2222−22−2222−2222000-22-2200002ζ−2ζ7−2ζ+2ζ700−2ζ3+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
χ4744-4-4000022−2222−22−2222−2222000-22-220000−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+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
χ4844-4-40000−2222−222222−2222−22000-22-2200002ζ3−2ζ5−2ζ3+2ζ5002ζ−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
χ4944-4-40000−2222−222222−2222−22000-22-220000−2ζ3+2ζ52ζ3−2ζ500−2ζ+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
χ5044-4-40000−2222−2222−2222−22220002-22-200002ζ−2ζ7−2ζ+2ζ700−2ζ3+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
χ5144-4-40000−2222−2222−2222−22220002-22-20000−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+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
χ524-44-404-402i22i2−2i2−2i2-4-44402i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ534-44-404-40−2i2−2i22i22i2-4-4440−2i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ544-44-40-4402i22i2−2i2−2i200000−2i22i20000002i2−2i200−2i22i20022-2-2-2-222000000000000000000000000
χ554-44-40-4402i22i2−2i2−2i200000−2i22i2000000−2i22i2002i2−2i200-2-22222-2-2000000000000000000000000
χ564-44-40-440−2i2−2i22i22i2000002i2−2i20000002i2−2i200−2i22i200-2-22222-2-2000000000000000000000000
χ574-44-40-440−2i2−2i22i22i2000002i2−2i2000000−2i22i2002i2−2i20022-2-2-2-222000000000000000000000000
χ584-4-44400-44i−4i−4i4i22−22−22220002i2−2i2−2i22i222−220000000000000000000000000000000000000000
χ594-4-44400-44i−4i−4i4i−222222−22000−2i22i22i2−2i2−22220000000000000000000000000000000000000000
χ604-4-44400-4−4i4i4i−4i22−22−2222000−2i22i22i2−2i222−220000000000000000000000000000000000000000
χ614-4-44400-4−4i4i4i−4i−222222−220002i2−2i2−2i22i2−22220000000000000000000000000000000000000000
χ624-4-44-4004000022−22−22220000000−2222000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ634-4-44-4004000022−22−22220000000−222200000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ644-4-44-40040000−222222−22000000022−22000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ654-4-44-40040000−222222−22000000022−2200000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000

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