Finite Group Databasebeta

← Group #104939

Character table — Group #104939

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222444444444444444488888888222244448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ922222222222222-2-2-2-2-2-222-2-2000000000000000022-2-2000000000000
χ1022222222222222-2-2-2-2-2-222-2-20000000000000000-2-222000000000000
χ11222222222222-2-22-222-2-2-2-22-200000000002200-2-20000000000000000
χ12222222222222-2-22-222-2-2-2-22-20000000000-2-200220000000000000000
χ13222222222222-2-2-22-2-222-2-2-22000000002200-2-2000000000000000000
χ14222222222222-2-2-22-2-222-2-2-2200000000-2-20022000000000000000000
χ1522222222-2-2-2-2222-2-2-222-2-22-200000000000000000000000000002i2i−2i−2i
χ1622222222-2-2-2-2222-2-2-222-2-22-20000000000000000000000000000−2i−2i2i2i
χ1722222222-2-2-2-222-2222-2-2-2-2-220000000000000000000000002i2i−2i−2i0000
χ1822222222-2-2-2-222-2222-2-2-2-2-22000000000000000000000000−2i−2i2i2i0000
χ1922222222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2022222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-2222222-2-2000000000000000000002i2i−2i−2i00000000
χ2222222222-2-2-2-2-2-2-2-2222222-2-200000000000000000000−2i−2i2i2i00000000
χ23222-2-2-22-22-22-20002002-2000-2i2i2−i2−i2i2i2−i2−i200002i−2i00000000002−22−20000
χ24222-2-2-22-22-22-20002002-2000-2i2i2−i2−i2i2i2−i2−i20000−2i2i0000000000−22−220000
χ25222-2-2-22-22-22-20002002-2000-2−i2−i2i2i2−i2−i2i2i200002i−2i0000000000−22−220000
χ26222-2-2-22-22-22-20002002-2000-2−i2−i2i2i2−i2−i2i2i20000−2i2i00000000002−22−20000
χ27222-2-2-22-2-22-22000200-22000-2i2i2−i2−i2−i2−i2i2i22-200000000000000i2−i2−i2i20000
χ28222-2-2-22-2-22-22000200-22000-2i2i2−i2−i2−i2−i2i2i2-2200000000000000−i2i2i2−i20000
χ29222-2-2-22-2-22-22000200-22000-2−i2−i2i2i2i2i2−i2−i22-200000000000000−i2i2i2−i20000
χ30222-2-2-22-2-22-22000200-22000-2−i2−i2i2i2i2i2−i2−i2-2200000000000000i2−i2−i2i20000
χ3122-22-2-2-222-2-2200202-20000-20i2−i2i2−i2i2−i2i2−i2002-20000000000000000i2−i2i2−i2
χ3222-22-2-2-222-2-2200202-20000-20i2−i2i2−i2i2−i2i2−i200-220000000000000000−i2i2−i2i2
χ3322-22-2-2-222-2-2200202-20000-20−i2i2−i2i2−i2i2−i2i2002-20000000000000000−i2i2−i2i2
χ3422-22-2-2-222-2-2200202-20000-20−i2i2−i2i2−i2i2−i2i200-220000000000000000i2−i2i2−i2
χ3522-22-2-2-22-222-20020-220000-20i2−i2i2−i2−i2i2−i2i20000002i−2i0000000000002−2−22
χ3622-22-2-2-22-222-20020-220000-20i2−i2i2−i2−i2i2−i2i2000000−2i2i000000000000−222−2
χ3722-22-2-2-22-222-20020-220000-20−i2i2−i2i2i2−i2i2−i20000002i−2i000000000000−222−2
χ3822-22-2-2-22-222-20020-220000-20−i2i2−i2i2i2−i2i2−i2000000−2i2i0000000000002−2−22
χ39444-4-4-44-44-44-4000-400-44000400000000000000000000000000000000
χ40444-4-4-44-4-44-44000-4004-4000400000000000000000000000000000000
χ4144-44-4-4-444-4-4400-40-4400004000000000000000000000000000000000
χ4244-44-4-4-44-444-400-404-400004000000000000000000000000000000000
χ4344-4-444-4-444-4-40000000000002-2-222-2-22000000000000000000000000
χ4444-4-444-4-444-4-4000000000000-222-2-222-2000000000000000000000000
χ4544-4-444-4-4-4-4440000000000002-2-22-222-2000000000000000000000000
χ4644-4-444-4-4-4-444000000000000-222-22-2-22000000000000000000000000
χ474-4444-4-4-400004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ484-4444-4-4-400004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ494-4444-4-4-40000−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ504-4444-4-4-40000−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ514-4-4-44-4440000000000004-40000000000000000000022−22000000000000
χ524-4-4-44-4440000000000004-400000000000000000000−2222000000000000
χ534-4-4-44-444000000000000-4400000000000000000022−2200000000000000
χ544-4-4-44-444000000000000-44000000000000000000−222200000000000000
χ558-88-8-88-88000000000000000000000000000000000000000000000000
χ568-8-88-888-8000000000000000000000000000000000000000000000000

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