Finite Group Databasebeta

← Group #145342

Character table — Group #145342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size111122444444444444816161616161616161616161616161616323232323232
order1222442444448888888448888881616161616161616244488
χ111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ61111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ9222222222222-2-2-2-2-2-2-222-2-2000000000000000000
χ10222222222222-2-2-2-2-2-2-2-2-222000000000000000000
χ1122222222-2-2-2-222-2-2-2-22000000002i2i−2i−2i0000000000
χ1222222222-2-2-2-222-2-2-2-2200000000−2i−2i2i2i0000000000
χ1322222222-2-2-2-2-2-22222-200000000000022-2-2000000
χ1422222222-2-2-2-2-2-22222-2000000000000-2-222000000
χ15222222-2-222-2-22222-2-2-20000000000000000002i−2i00
χ16222222-2-222-2-22222-2-2-2000000000000000000−2i2i00
χ17222222-2-222-2-2-2-2-2-222200002i2i−2i−2i00000000000000
χ18222222-2-222-2-2-2-2-2-22220000−2i−2i2i2i00000000000000
χ19222222-2-2-2-22222-2-222-2000000000000000000002-2
χ20222222-2-2-2-22222-2-222-200000000000000000000-22
χ21222222-2-2-2-222-2-222-2-2200000000000000002-20000
χ22222222-2-2-2-222-2-222-2-220000000000000000-220000
χ232222-2-2-222-2-220000000002i−2i00002−22−2i2−i2i2−i2000000
χ242222-2-2-222-2-220000000002i−2i0000−22−22−i2i2−i2i2000000
χ252222-2-2-222-2-22000000000−2i2i00002−22−2−i2i2−i2i2000000
χ262222-2-2-222-2-22000000000−2i2i0000−22−22i2−i2i2−i2000000
χ272222-2-2-22-222-200000002-2000000i2−i2−i2i2i2−i2−i2i2000000
χ282222-2-2-22-222-200000002-2000000−i2i2i2−i2−i2i2i2−i2000000
χ292222-2-2-22-222-20000000-22000000i2−i2−i2i2−i2i2i2−i2000000
χ302222-2-2-22-222-20000000-22000000−i2i2i2−i2i2−i2−i2i2000000
χ314444-4-44-44-44-400000000000000000000000000000
χ324444-4-44-4-44-4400000000000000000000000000000
χ3344-4-4-440000004i−4i0000000002ζ−2ζ2ζ3−2ζ300000000000000
χ3444-4-4-440000004i−4i000000000−2ζ2ζ−2ζ32ζ300000000000000
χ3544-4-4-44000000−4i4i0000000002ζ3−2ζ32ζ−2ζ00000000000000
χ3644-4-4-44000000−4i4i000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ3788-8-88-800000000000000000000000000000000000
χ388-88-80000000000004i2−4i200000000000000000000000
χ398-88-8000000000000−4i24i200000000000000000000000
χ408-8-88000000000042−420000000000000000000000000
χ418-8-880000000000−42420000000000000000000000000

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