Finite Group Databasebeta

← Group #143906

Character table — Group #143906

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size111122222244444444888888888816161616161616163232323232323232
order12224488882444448888161616161616161624881616161644448888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-111
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ922222222222-2-22-2-222-2-200000000000022-2-200000000
χ1022222222222-2-22-2-222-2-2000000000000-2-22200000000
χ112222222222-22-2-22-2-2-22-20000000000000000020-20000
χ122222222222-22-2-22-2-2-22-200000000000000000-2020000
χ132222222222-2-22-2-22-2-2-22000000000000000020-200000
χ142222222222-2-22-2-22-2-2-220000000000000000-20200000
χ15222222-2-2-2-2222222-2-2-2-20000000022-2-2000000000000
χ16222222-2-2-2-2222222-2-2-2-200000000-2-222000000000000
χ17222222-2-2-2-22-2-22-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000
χ18222222-2-2-2-22-2-22-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000
χ19222222-2-2-2-2-22-2-22-222-22000000000000000000002-200
χ20222222-2-2-2-2-22-2-22-222-2200000000000000000000-2200
χ21222222-2-2-2-2-2-22-2-22222-200000000000000000000002-2
χ22222222-2-2-2-2-2-22-2-22222-20000000000000000000000-22
χ232222-2-20000-2222-2-20000i2i2−i2−i2i2i2−i2−i2002i−2i2−22−200000000
χ242222-2-20000-2222-2-20000i2i2−i2−i2i2i2−i2−i200−2i2i−22−2200000000
χ252222-2-20000-2222-2-20000−i2−i2i2i2−i2−i2i2i2002i−2i−22−2200000000
χ262222-2-20000-2222-2-20000−i2−i2i2i2−i2−i2i2i200−2i2i2−22−200000000
χ272222-2-20000-2-2-2222000022−2−2−2−2222-2002−2−2200000000
χ282222-2-20000-2-2-2222000022−2−2−2−222-2200−222−200000000
χ292222-2-20000-2-2-22220000−2−22222−2−22-200−222−200000000
χ302222-2-20000-2-2-22220000−2−22222−2−2-22002−2−2200000000
χ314444-4-4000044-4-4-440000000000000000000000000000
χ324444-4-400004-44-44-40000000000000000000000000000
χ334-4-444-400000000004i−4i002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ344-4-444-400000000004i−4i00−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ354-4-444-40000000000−4i4i002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ364-4-444-40000000000−4i4i00−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ374-4-44-4444-4-400000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ384-4-44-4444-4-40000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ394-4-44-44-4-44400000000002-2-222-2-220000000000000000
χ404-4-44-44-4-4440000000000-222-2-222-20000000000000000
χ4188-8-80042−4242−420000000000000000000000000000000000
χ4288-8-800−4242−42420000000000000000000000000000000000
χ438-88-80042−42−42420000000000000000000000000000000000
χ448-88-800−424242−420000000000000000000000000000000000

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