Finite Group Databasebeta

← Group #504378

Character table — Group #504378

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444888888888888888888888161616161616161616161616163232
order122222444488884444888816161616244444448881616161616161616161622244444888161648
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1
χ41111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ5111111111111111111-1-1111111-1-11111-1-111-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-111-1-111
χ7111111111111111111-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1111111-11111-1-1
χ911111111111111-1-1-1-111111111-1-1111111-1-1111-1-1-1-11111-1-111-1-1-1-1-111-1-1-11
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-1-1-1111111-1-11111-1-1-1-1-11-1
χ1111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-111111-1
χ1211111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-1-11111-1-1-1-11111-1-111-1-1-111-11
χ1311111111111111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1111-1
χ1411111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111111-11
χ1511111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-11
χ1611111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-11-1
χ172222222222-2-2-2-2222222-2-20000220000-2-2-2-22000000000000000000-2000000
χ182222222222-2-2-2-22222-2-2-2-20000-2-2000022-2-2-20000000000000000002000000
χ192222222222-2-2-2-2-2-2-2-222-2-20000-2-20000-2-22220000000000000000002000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-200002200002222-2000000000000000000-2000000
χ212222-2-22-22-22222000000-2-222220022-2-200000-2-200000000002-200000000000
χ222222-2-22-22-22222000000-2-2222200-2-22200000-2-20000000000-2200000000000
χ232222-2-22-22-22222000000-2-2-2-2-2-20022-2-200000220000000000-2200000000000
χ242222-2-22-22-22222000000-2-2-2-2-2-200-2-222000002200000000002-200000000000
χ252222-2-2-22-22000022-2-2220022−2−2-2200000000-22−222−2−222−2−2000000000002−200
χ262222-2-2-22-22000022-2-22200−2−222-2200000000-2−22−2−222−2−22200000000000−2200
χ272222-2-2-22-22000022-2-2-2-20022−2−22-20000000022−222−2−2−2−22200000000000−2200
χ282222-2-2-22-22000022-2-2-2-200−2−2222-2000000002−22−2−22222−2−2000000000002−200
χ292222-2-2-22-220000-2-222220022−2−22-200000000-22−2−2−22222−2−200000000000−2200
χ302222-2-2-22-220000-2-2222200−2−2222-200000000-2−2222−2−2−2−222000000000002−200
χ312222-2-2-22-220000-2-222-2-20022−2−2-220000000022−2−2−222−2−222000000000002−200
χ322222-2-2-22-220000-2-222-2-200−2−222-22000000002−2222−2−222−2−200000000000−2200
χ3322-2-22-2-2-22222-2-22i−2i2i−2i00-220000000000002i−2i000000000000000002i−2i02-20000
χ3422-2-22-2-2-22222-2-22i−2i2i−2i00-220000000000002i−2i00000000000000000−2i2i0-220000
χ3522-2-22-2-2-22222-2-2−2i2i−2i2i00-22000000000000−2i2i000000000000000002i−2i0-220000
χ3622-2-22-2-2-22222-2-2−2i2i−2i2i00-22000000000000−2i2i00000000000000000−2i2i02-20000
χ3722-2-22-2-2-222-2-2222i−2i2i−2i002-20000002i−2i2i−2i00−2i2i000000000002-20000000000000
χ3822-2-22-2-2-222-2-2222i−2i2i−2i002-2000000−2i2i−2i2i00−2i2i00000000000-220000000000000
χ3922-2-22-2-2-222-2-222−2i2i−2i2i002-20000002i−2i2i−2i002i−2i00000000000-220000000000000
χ4022-2-22-2-2-222-2-222−2i2i−2i2i002-2000000−2i2i−2i2i002i−2i000000000002-20000000000000
χ4122-2-2-22-222-2-2-222000000-220000002i−2i−2i2i00000002-22-2000000002i−2i000000000
χ4222-2-2-22-222-2-2-222000000-220000002i−2i−2i2i0000000-22-2200000000−2i2i000000000
χ4322-2-2-22-222-2-2-222000000-22000000−2i2i2i−2i00000002-22-200000000−2i2i000000000
χ4422-2-2-22-222-2-2-222000000-22000000−2i2i2i−2i0000000-22-22000000002i−2i000000000
χ45444444-4-4-4-40000000000002222−22−2200000000000−222200000000000000000000000
χ46444444-4-4-4-4000000000000−22−2222220000000000022−2200000000000000000000000
χ474444-4-44-44-4-4-4-4-4000000440000000000000000000000000000000000000000
χ4844-4-44-444-4-40000000000000000000000000000022−22−22220000000000000000000
χ4944-4-44-444-4-400000000000000000000000000000−222222−220000000000000000000
χ5044-4-4-444-4-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ5144-4-4-444-4-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5244-4-4-44-444-444-4-40000004-40000000000000000000000000000000000000000
χ534-44-400000022−2222−2200002i2−2i2002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000002i−2i000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000
χ544-44-400000022−2222−2200002i2−2i200−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000002i−2i000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000
χ554-44-400000022−2222−220000−2i22i2002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000−2i2i000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000
χ564-44-400000022−2222−220000−2i22i200−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000−2i2i000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000
χ574-44-4000000−2222−222200002i2−2i2002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000−2i2i000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000
χ584-44-4000000−2222−222200002i2−2i200−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000−2i2i000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000
χ594-44-4000000−2222−22220000−2i22i2002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000002i−2i000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000
χ604-44-4000000−2222−22220000−2i22i200−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000002i−2i000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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