Finite Group Databasebeta

← Group #492671

Character table — Group #492671

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444444444444444448888888816161616161616161616161632323232
order1222444488888888488888888161616161616161616161616161616162224444424888888161616162244
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111111-1-1-1-1-1-11-11-1
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
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-11111111-11-1
χ911111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-111-1-11-1-11
χ1011111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-11-1-1-1-1-1-111-111-1
χ1111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1111111-1-1-111-1
χ1211111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1-1111-1-11
χ1311111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-111-1-11111-1-1
χ1411111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-11-11-1-11111-1-1-1-111
χ1511111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-111-1-1-1-111-1-111
χ1611111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1111-1-111-1-111-1-1
χ17222222222222-2-2-2-2222-2-2-2-2-2-200000000000000000022002200-2-2000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2000000000000000000-2-200-2-20022000000000000
χ1922222222-2-2-2-2-2-2-2-22-2-22222-2-20000000000000000002200-2-200-22000000000000
χ2022222222-2-2-2-2-2-2-2-22-2-22222-2-2000000000000000000-2-20022002-2000000000000
χ2122222-2-2222220000-2-2-20000002222−2−2−2−22222−2−2−2−2002-200-22000000002−22−20000
χ2222222-2-2222220000-2-2-20000002222−2−2−2−22222−2−2−2−200-22002-200000000−22−220000
χ2322222-2-2222220000-2-2-2000000−2−2−2−22222−2−2−2−22222002-200-2200000000−22−220000
χ2422222-2-2222220000-2-2-2000000−2−2−2−22222−2−2−2−2222200-22002-2000000002−22−20000
χ2522222-2-22-2-2-2-20000-2220000002222−2−2−2−2−2−2−2−22222002-2002-2000000002−2−220000
χ2622222-2-22-2-2-2-20000-2220000002222−2−2−2−2−2−2−2−2222200-2200-2200000000−222−20000
χ2722222-2-22-2-2-2-20000-222000000−2−2−2−222222222−2−2−2−2002-2002-200000000−222−20000
χ2822222-2-22-2-2-2-20000-222000000−2−2−2−222222222−2−2−2−200-2200-22000000002−2−220000
χ292222-222-200002222-2000000-2-222-2-222-2-20000000022002200-2-200000000000000
χ302222-222-200002222-2000000-2-222-2-222-2-200000000-2-200-2-2002200000000000000
χ312222-222-200002222-2000000-2-2-2-222-2-222000000002200-2-2002-200000000000000
χ322222-222-200002222-2000000-2-2-2-222-2-22200000000-2-2002200-2200000000000000
χ3322-2-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i2002i−2i002i−2i0022−2−222−2−22-2002i−2i000000i2−i22−200000000
χ3422-2-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i2002i−2i002i−2i0022−2−222−2−2-2200−2i2i000000−i2i2−2200000000
χ3522-2-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i200−2i2i00−2i2i00−2−222−2−2222-200−2i2i000000i2−i2−2200000000
χ3622-2-202-20i2i2−i2−i222-2-20i2−i2i2i2−i2−i200−2i2i00−2i2i00−2−222−2−222-22002i−2i000000−i2i22−200000000
χ3722-2-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i2002i−2i002i−2i00−2−222−2−2222-2002i−2i000000−i2i2−2200000000
χ3822-2-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i2002i−2i002i−2i00−2−222−2−222-2200−2i2i000000i2−i22−200000000
χ3922-2-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i200−2i2i00−2i2i0022−2−222−2−22-200−2i2i000000−i2i22−200000000
χ4022-2-202-20−i2−i2i2i222-2-20−i2i2−i2−i2i2i200−2i2i00−2i2i0022−2−222−2−2-22002i−2i000000i2−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
χ4444-4-404-402i22i2−2i2−2i2-4-44402i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ4544-4-404-40−2i2−2i22i22i2-4-4440−2i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ4644-4-40-4402i22i2−2i2−2i200000−2i22i20000002i2−2i200−2i22i20022-2-2-2-222000000000000000000000000
χ4744-4-40-4402i22i2−2i2−2i200000−2i22i2000000−2i22i2002i2−2i200-2-22222-2-2000000000000000000000000
χ4844-4-40-440−2i2−2i22i22i2000002i2−2i20000002i2−2i200−2i22i200-2-22222-2-2000000000000000000000000
χ4944-4-40-440−2i2−2i22i22i2000002i2−2i2000000−2i22i2002i2−2i20022-2-2-2-222000000000000000000000000
χ504-44-4400-44i−4i4i−4i22−2222−220002i2−2i22i2−2i222−220000000000000000000000000000000000000000
χ514-44-4400-44i−4i4i−4i−2222−2222000−2i22i2−2i22i2−22220000000000000000000000000000000000000000
χ524-44-4400-4−4i4i−4i4i22−2222−22000−2i22i2−2i22i222−220000000000000000000000000000000000000000
χ534-44-4400-4−4i4i−4i4i−2222−22220002i2−2i22i2−2i2−22220000000000000000000000000000000000000000
χ544-44-4-4004000022−2222−220000000−2222000000002ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ554-44-4-4004000022−2222−220000000−222200000000−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ564-44-4-40040000−2222−2222000000022−22000000002ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ574-44-4-40040000−2222−2222000000022−2200000000−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ584-4-44000022−22−222222−22−22220002-2-2200002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ5ζ+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−ζ7000000000000000000000000
χ594-4-44000022−22−222222−22−22220002-2-220000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5−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+ζ7000000000000000000000000
χ604-4-44000022−22−2222−222222−22000-222-200002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ7ζ−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+ζ7000000000000000000000000
χ614-4-44000022−22−2222−222222−22000-222-20000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7−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−ζ7000000000000000000000000
χ624-4-440000−222222−2222−22−2222000-222-200002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ5−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+ζ7000000000000000000000000
χ634-4-440000−222222−2222−22−2222000-222-20000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5ζ+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−ζ7000000000000000000000000
χ644-4-440000−222222−22−222222−220002-2-2200002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ7−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−ζ7000000000000000000000000
χ654-4-440000−222222−22−222222−220002-2-220000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7ζ−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+ζ7000000000000000000000000

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