Finite Group Databasebeta

← Group #501370

Character table — Group #501370

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size112222222224444444888888888888888888888816161616161616161616161616163232
order1222244448822448882244888888161616161616161616161616224488888888161644
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1
χ911111111111-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-11-111-1-111-1-1-1-1-11
χ1011111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1-1-111111-1
χ1111111111111-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111-1
χ1211111111111-1-1-1-11111111-1-1-1-111-1-1-1-111111111-1-1-11-1-111-1-111-1-1-11
χ1311111111111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-11111111-1-1-111-1-111-1-11-1
χ1411111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-11111-1-111-11
χ1511111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-1-1-11111-11
χ1611111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1111-1-111-1-1-1-11-1
χ17222222222-2-22222-2-2-20000-2-2222200000000000000-2-2000000000000
χ18222222222-2-22222-2-2-20000-2-2-2-2-2-20000000000000022000000000000
χ19222222222-2-2-2-2-2-2-2-2-200002222-2-200000000000000-22000000000000
χ20222222222-2-2-2-2-2-2-2-2-2000022-2-222000000000000002-2000000000000
χ2122222-2-2-2-2002-22-20000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−20000000000002−200
χ2222222-2-2-2-2002-22-20000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222000000000000−2200
χ2322222-2-2-2-2002-22-2000000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−2−222000000000000−2200
χ2422222-2-2-2-2002-22-2000000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222−2−20000000000002−200
χ2522222-2-2-2-200-22-220000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2000000000000−2200
χ2622222-2-2-2-200-22-220000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−2220000000000002−200
χ2722222-2-2-2-200-22-22000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−2220000000000002−200
χ2822222-2-2-2-200-22-22000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2000000000000−2200
χ29222-2-222-2-2-2-200002-222-22-20000002i−2i2i−2i00000000000000002i−2i000000
χ30222-2-222-2-2-2-200002-222-22-2000000−2i2i−2i2i0000000000000000−2i2i000000
χ31222-2-222-2-2-2-200002-22-22-220000002i−2i2i−2i0000000000000000−2i2i000000
χ32222-2-222-2-2-2-200002-22-22-22000000−2i2i−2i2i00000000000000002i−2i000000
χ3322-22-22-22-2-2-20000-2222-2-2200000000002i−2i2i−2i000000000000002i−2i0000
χ3422-22-22-22-2-2-20000-2222-2-220000000000−2i2i−2i2i00000000000000−2i2i0000
χ3522-22-22-22-2-2-20000-222-222-200000000002i−2i2i−2i00000000000000−2i2i0000
χ3622-22-22-22-2-2-20000-222-222-20000000000−2i2i−2i2i000000000000002i−2i0000
χ3722-2-222-2-22222-2-22-2-2222-2-22-200000000000000002-200000000000000
χ3822-2-222-2-22222-2-22-2-22-2-2222-20000000000000000-2200000000000000
χ3922-2-222-2-2222-222-2-2-2222-2-2-220000000000000000-2200000000000000
χ4022-2-222-2-2222-222-2-2-22-2-222-2200000000000000002-200000000000000
χ4122-2-222-2-22-2-22-2-2222-20000-22000000000000000000002i−2i2i−2i00000000
χ4222-2-222-2-22-2-22-2-2222-20000-2200000000000000000000−2i2i−2i2i00000000
χ4322-2-222-2-22-2-2-222-222-200002-2000000000000000000002i−2i−2i2i00000000
χ4422-2-222-2-22-2-2-222-222-200002-200000000000000000000−2i2i2i−2i00000000
χ45444-4-444-4-4440000-44-400000000000000000000000000000000000000
χ46444-4-4-4-444000000000000000000022−22−2222000000000000000000000000
χ47444-4-4-4-4440000000000000000000−222222−22000000000000000000000000
χ4844-44-44-44-44400004-4-400000000000000000000000000000000000000
χ4944-44-4-44-440000000000000000000000022−22−222200000000000000000000
χ5044-44-4-44-4400000000000000000000000−222222−2200000000000000000000
χ5144-4-44-444-40044-4-400000000000000000000000000000000000000000
χ5244-4-44-444-400-4-44400000000000000000000000000000000000000000
χ538-8000000042−4200000000000000000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000
χ548-8000000042−420000000000000000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000
χ558-80000000−424200000000000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000
χ568-80000000−42420000000000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000

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