Finite Group Databasebeta

← Group #133039

Character table — Group #133039

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244488888888888888888881616161616161616161616161632323232
order12222222244224444444444444444444444444488884488
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111-1-11111-1-1-1-1-1-1-1-11-11-111111-1-1-1-1-111-1-1
χ4111111111111111-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-11-11111-1-111
χ51111111111111-1-11111-1-111-1-1-1-1-1-11-1-111111-11-1-1-1-1-1-111
χ61111111111111-1-11111-1-111-1-1-1-1-1-11-1-11-1-1-1-1-11111111-1-1
χ71111111111111-1-1-1-111-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ81111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ911111-1-11-1-1-11-1111111-1-1-1-1-1-111-1-1-11-11ii−i−i1-1ii−i−ii−ii−i
χ1011111-1-11-1-1-11-1111111-1-1-1-1-1-111-1-1-11-11−i−iii1-1−i−iii−ii−ii
χ1111111-1-11-1-1-11-111-1-111-1-11111-1-111-1-1-1-1ii−i−i11−i−iiii−i−ii
χ1211111-1-11-1-1-11-111-1-111-1-11111-1-111-1-1-1-1−i−iii11ii−i−i−iii−i
χ1311111-1-11-1-1-11-1-1-1111111-1-111-1-111-1-111ii−i−i-1-1−i−iii−iii−i
χ1411111-1-11-1-1-11-1-1-1111111-1-111-1-111-1-111−i−iii-1-1ii−i−ii−i−ii
χ1511111-1-11-1-1-11-1-1-1-1-1111111-1-111-1-1-111-1ii−i−i-11ii−i−i−ii−ii
χ1611111-1-11-1-1-11-1-1-1-1-1111111-1-111-1-1-111-1−i−iii-11−i−iiii−ii−i
χ1722222222222-2-200222-20022000000-200-200000-200000000
χ1822222222222-2-200-2-22-200-2-2000000-200200000200000000
χ19222222222-2-2222200-2-22200000000-20-200000-2000000000
χ20222222222-2-222-2-200-2-2-2-200000000-202000002000000000
χ21222222222-2-2-2-20000-22000022-2-2-2-2220000000000000000
χ22222222222-2-2-2-20000-220000-2-222222-20000000000000000
χ2322222-2-22-2222-22200-2-2-2-20000000020200000-2000000000
χ2422222-2-22-2222-2-2-200-2-2220000000020-2000002000000000
χ2522222-2-22-222-220000-2200002222-2-2-2-20000000000000000
χ2622222-2-22-222-220000-220000-2-2-2-222-220000000000000000
χ2722222-2-22-2-2-2-2200222-200-2-2000000200-200000200000000
χ2822222-2-22-2-2-2-2200-2-22-20022000000200200000-200000000
χ294444-444-4-40000000000000000000000002-22-20000000000
χ304444-444-4-4000000000000000000000000-22-220000000000
χ314444-4-4-4-440000000000000000000000002i−2i−2i2i0000000000
χ324444-4-4-4-44000000000000000000000000−2i2i2i−2i0000000000
χ3344-4-4-400404i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3444-4-4-400404i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3544-4-4-40040−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3644-4-4-40040−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ374-44-404-40000002i−2i2i−2i002i−2i2i−2i002-22-2000000000000000000
χ384-44-404-40000002i−2i−2i2i002i−2i−2i2i00-22-22000000000000000000
χ394-44-404-4000000−2i2i2i−2i00−2i2i2i−2i00-22-22000000000000000000
χ404-44-404-4000000−2i2i−2i2i00−2i2i−2i2i002-22-2000000000000000000
χ414-44-40-440000002i−2i2i−2i00−2i2i−2i2i002-2-22000000000000000000
χ424-44-40-440000002i−2i−2i2i00−2i2i2i−2i00-222-2000000000000000000
χ434-44-40-44000000−2i2i2i−2i002i−2i−2i2i00-222-2000000000000000000
χ444-44-40-44000000−2i2i−2i2i002i−2i2i−2i002-2-22000000000000000000
χ4588-8-8800-8000000000000000000000000000000000000000
χ468-8-8800000000000000000004i−4i0000000000000000000000
χ478-8-880000000000000000000−4i4i0000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.