Finite Group Databasebeta

← Group #501809

Character table — Group #501809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444888888888888888888888161616161616161616161616163232
order122222444488882244888816161616244444448881616161616161616161622244444888161648
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1
χ41111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-111
χ5111111111111111111-1-1111111-1-11111-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1
χ6111111111111111111-1-1111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-111
χ7111111111111111111-1-111-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-11111
χ8111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-11111-1-1
χ911111111111111-1-1-1-111111111-1-11111111-1-111-1-1-1-111111-1-11-1-1-1-1-111-1-1-11
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-1-1-11111-111-11111-1-1-1-1-11-1
χ1111111111111111-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111111-1
χ1211111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11-1-111111-1-1-111-11
χ1311111111111111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-11-1-1111-1
χ1411111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11111111-11
χ1511111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111111111-111-111-1-11-1-1-1-1-11
χ1611111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111111-1-11-1
χ172222222222-2-2-2-2222222-2-20000220000-2-22-2-2000000000000000000-2000000
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
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2000022000022-222000000000000000000-2000000
χ212222-2-22-22-22222000000-2-222220022-2-200000-2-200000000-200200000000000
χ222222-2-22-22-22222000000-2-2222200-2-22200000-2-200000000200-200000000000
χ232222-2-22-22-22222000000-2-2-2-2-2-20022-2-2000002200000000200-200000000000
χ242222-2-22-22-22222000000-2-2-2-2-2-200-2-222000002200000000-200200000000000
χ252222-2-2-22-22000022-2-2220022−2−2-22000000-2002−222−2−222−2−2000000000002−200
χ262222-2-2-22-22000022-2-22200−2−222-22000000-200−22−2−222−2−22200000000000−2200
χ272222-2-2-22-22000022-2-2-2-20022−2−22-20000002002−222−2−2−2−22200000000000−2200
χ282222-2-2-22-22000022-2-2-2-200−2−2222-2000000200−22−2−22222−2−2000000000002−200
χ292222-2-2-22-220000-2-222220022−2−22-2000000-2002−2−2−22222−2−200000000000−2200
χ302222-2-2-22-220000-2-2222200−2−2222-2000000-200−2222−2−2−2−222000000000002−200
χ312222-2-2-22-220000-2-222-2-20022−2−2-220000002002−2−2−222−2−222000000000002−200
χ322222-2-2-22-220000-2-222-2-200−2−222-22000000200−2222−2−222−2−200000000000−2200
χ3322-2-22-2-2-22222-2-20000002-20000002i−2i2i−2i00000002i−2i2i−2i000002-2000000000000
χ3422-2-22-2-2-22222-2-20000002-20000002i−2i2i−2i0000000−2i2i−2i2i00000-22000000000000
χ3522-2-22-2-2-22222-2-20000002-2000000−2i2i−2i2i00000002i−2i2i−2i00000-22000000000000
χ3622-2-22-2-2-22222-2-20000002-2000000−2i2i−2i2i0000000−2i2i−2i2i000002-2000000000000
χ3722-2-2-22-222-222-2-22-22-200-220000002i−2i−2i2i0002-200000000000000002i−2i0000000
χ3822-2-2-22-222-222-2-22-22-200-22000000−2i2i2i−2i0002-20000000000000000−2i2i0000000
χ3922-2-2-22-222-222-2-2-22-2200-220000002i−2i−2i2i000-220000000000000000−2i2i0000000
χ4022-2-2-22-222-222-2-2-22-2200-22000000−2i2i2i−2i000-2200000000000000002i−2i0000000
χ4122-2-2-22-222-2-2-2222-22-2002-20000000000000-22000000000000002i−2i0002i−2i0000
χ4222-2-2-22-222-2-2-2222-22-2002-20000000000000-2200000000000000−2i2i000−2i2i0000
χ4322-2-2-22-222-2-2-222-22-22002-200000000000002-2000000000000002i−2i000−2i2i0000
χ4422-2-2-22-222-2-2-222-22-22002-200000000000002-200000000000000−2i2i0002i−2i0000
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
χ4844-4-44-444-4-400004-4-4400000000000000000000000000000000000000000000
χ4944-4-44-444-4-40000-444-400000000000000000000000000000000000000000000
χ5044-4-44-4-4-444-4-444000000-440000000000000000000000000000000000000000
χ5144-4-4-444-4-44000000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5244-4-4-444-4-4400000000000000000000000000000−2i22i22i2−2i20000000000000000000
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+2ζ7000000−2i2i000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000
χ584-44-4000000−2222−222200002i2−2i200−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000−2i2i000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ594-44-4000000−2222−22220000−2i22i2002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000002i−2i000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ604-44-4000000−2222−22220000−2i22i200−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000002i−2i000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−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.