Finite Group Databasebeta

← Group #133014

Character table — Group #133014

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244488888888888888888881616161616161616161616161632323232
order12222222244224444444444444444424444444488888888
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-11-11111-1-111
χ511111111111-1-1111-1-11111-1-111-1-111-1-1-11111-111111-1-1-1-1
χ611111111111-1-1111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-11111
χ711111111111-1-1111-1-1-1-1-1-111-1-1111111-11111-1-1-1-1-1-1-1-111
χ811111111111-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1111111-1-1
χ911111-1-11-1-1-111111-1-111-1-111-1-1-1-1-1-1-111ii−i−i-11ii−i−ii−ii−i
χ1011111-1-11-1-1-111111-1-111-1-111-1-1-1-1-1-1-111−i−iii-11−i−iii−ii−ii
χ1111111-1-11-1-1-111111-1-1-1-111-1-11111-1-11-11ii−i−i-1-1−i−iiii−i−ii
χ1211111-1-11-1-1-111111-1-1-1-111-1-11111-1-11-11−i−iii-1-1ii−i−i−iii−i
χ1311111-1-11-1-1-1-1-11111111-1-1-1-1-1-111-1-11-1-1ii−i−i11ii−i−i−ii−ii
χ1411111-1-11-1-1-1-1-11111111-1-1-1-1-1-111-1-11-1-1−i−iii11−i−iiii−ii−i
χ1511111-1-11-1-1-1-1-111111-1-1111111-1-1-1-1-11-1ii−i−i1-1−i−iii−iii−i
χ1611111-1-11-1-1-1-1-111111-1-1111111-1-1-1-1-11-1−i−iii1-1ii−i−ii−i−ii
χ172222222222222-22-2220000000000-2-200-20000-2000000000
χ1822222222222-2-2-22-2-2-20000000000-2-200200002000000000
χ19222222222-2-2002-2-20000002200222-2-2-2000000000000000
χ20222222222-2-2002-2-2000000-2-200-2-22-222000000000000000
χ21222222222-2-200-2-2200222200-2-200-2200000000-200000000
χ22222222222-2-200-2-2200-2-2-2-2002200-2200000000200000000
χ2322222-2-22-222002-2-20000002200-2-2-222-2000000000000000
χ2422222-2-22-222002-2-2000000-2-20022-22-22000000000000000
χ2522222-2-22-22200-2-220022-2-20022002-200000000-200000000
χ2622222-2-22-22200-2-2200-2-22200-2-2002-200000000200000000
χ2722222-2-22-2-2-222-22-2-2-200000000002200-200002000000000
χ2822222-2-22-2-2-2-2-2-22-2220000000000220020000-2000000000
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
χ334-44-4-400404i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ344-44-4-400404i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ354-44-4-40040−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ364-44-4-40040−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ374-4-4404-400002-20002-22-22-22-2002-20000000000000000000
χ384-4-4404-400002-20002-2-22-22-2200-220000000000000000000
χ394-4-4404-40000-22000-222-22-2-2200-220000000000000000000
χ404-4-4404-40000-22000-22-22-222-2002-20000000000000000000
χ414-4-440-4400002-2000-222-2-222-200-220000000000000000000
χ424-4-440-4400002-2000-22-222-2-22002-20000000000000000000
χ434-4-440-440000-220002-22-2-22-22002-20000000000000000000
χ444-4-440-440000-220002-2-222-22-200-220000000000000000000
χ4588-8-8000000000000000000004-4000000000000000000000
χ4688-8-800000000000000000000-44000000000000000000000
χ478-88-8800-8000000000000000000000000000000000000000

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