Finite Group Databasebeta

← Group #236608

Character table — Group #236608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222244444888888881616161616161616161611112222444448888888816161616161616161616
order12224444244448888888824444488882222444424444888888882444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-11-1-1-1-1-1-11111111111111111111111-1-11-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-11-1-11-111-1-111111111111111111-1-1-1-1-11-1-11-111-1-1
χ411111111111111111-1-1-1-1-1-11-1-11-1-11111111111111111111-1-1-1-1-1-11-1-11-1-111
χ51111111111111-1-1-1-11111-111-111-1-1-1-11111111111111-1-1-1-11111-111-111-1-1-1-1
χ61111111111111-1-1-1-11111-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111-1-1-1-1-1-1-1-111-111-1-1-1111111111111111-1-1-1-1-1-1-1-111-111-1-1-111
χ81111111111111-1-1-1-1-1-1-1-11-111-1111-1-11111111111111-1-1-1-1-1-1-1-11-111-1111-1-1
χ922222222-22-2-2-2000000000000002-20022222222-22-2-2-2000000000000002-200
χ1022222222-22-2-2-200000000000000-220022222222-22-2-2-200000000000000-2200
χ11222222-2-22-2-22-20000000000200-20000222222-2-22-2-22-20000000000200-20000
χ12222222-2-22-2-22-20000000000-20020000222222-2-22-2-22-20000000000-20020000
χ13222222-2-2-2-22-2200000000200-2000000222222-2-2-2-22-2200000000200-2000000
χ14222222-2-2-2-22-2200000000-2002000000222222-2-2-2-22-2200000000-2002000000
χ152222-2-2222-2-2-2200000000000000002-22222-2-2222-2-2-2200000000000000002-2
χ162222-2-2222-2-2-220000000000000000-222222-2-2222-2-2-220000000000000000-22
χ172222-2-222-2-222-2000022-2-200000000002222-2-222-2-222-2000022-2-20000000000
χ182222-2-222-2-222-20000-2-22200000000002222-2-222-2-222-20000-2-2220000000000
χ192222-2-2-2-2222-2-22i2i−2i−2i000000000000002222-2-2-2-2222-2-22i2i−2i−2i00000000000000
χ202222-2-2-2-2222-2-2−2i−2i2i2i000000000000002222-2-2-2-2222-2-2−2i−2i2i2i00000000000000
χ212222-2-2-2-2-22-222000000000200-2000002222-2-2-2-2-22-222000000000200-200000
χ222222-2-2-2-2-22-222000000000-2002000002222-2-2-2-2-22-222000000000-200200000
χ2344-4-44-4000000000002-22-2000000000044-4-44-4000000000002-22-20000000000
χ2444-4-44-400000000000-22-22000000000044-4-44-400000000000-22-220000000000
χ2544-4-4-44000000000002-2-22000000000044-4-4-44000000000002-2-220000000000
χ2644-4-4-4400000000000-222-2000000000044-4-4-4400000000000-222-20000000000
χ274-44-4004i−4i000002ζ−2ζ2ζ3−2ζ3000000000000004-44-4004i−4i000002ζ−2ζ2ζ3−2ζ300000000000000
χ284-44-4004i−4i00000−2ζ2ζ−2ζ32ζ3000000000000004-44-4004i−4i00000−2ζ2ζ−2ζ32ζ300000000000000
χ294-44-400−4i4i000002ζ3−2ζ32ζ−2ζ000000000000004-44-400−4i4i000002ζ3−2ζ32ζ−2ζ00000000000000
χ304-44-400−4i4i00000−2ζ32ζ3−2ζ2ζ000000000000004-44-400−4i4i00000−2ζ32ζ3−2ζ2ζ00000000000000
χ318-8-880000000000000000000000000008-8-88000000000000000000000000000
χ321111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ331111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ3411111111111111111-1-1-1-1-11-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-11-1-111
χ3511111111111111111-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1
χ361111111111111-1-1-1-11111-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-11111
χ371111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ381111111111111-1-1-1-1-1-1-1-111-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-1
χ391111111111111-1-1-1-1-1-1-1-11-111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11-1-1-111
χ4022222222-22-2-2-2000000000000002-200-2-2-2-2-2-2-2-22-222200000000000000-2200
χ4122222222-22-2-2-200000000000000-2200-2-2-2-2-2-2-2-22-2222000000000000002-200
χ42222222-2-22-2-22-20000000000200-20000-2-2-2-2-2-222-222-220000000000-20020000
χ43222222-2-22-2-22-20000000000-20020000-2-2-2-2-2-222-222-220000000000200-20000
χ44222222-2-2-2-22-2200000000200-2000000-2-2-2-2-2-22222-22-200000000-2002000000
χ45222222-2-2-2-22-2200000000-2002000000-2-2-2-2-2-22222-22-200000000200-2000000
χ462222-2-2222-2-2-2200000000000000002-2-2-2-2-222-2-2-2222-20000000000000000-22
χ472222-2-2222-2-2-220000000000000000-22-2-2-2-222-2-2-2222-200000000000000002-2
χ482222-2-222-2-222-2000022-2-20000000000-2-2-2-222-2-222-2-220000-2-2220000000000
χ492222-2-222-2-222-20000-2-2220000000000-2-2-2-222-2-222-2-22000022-2-20000000000
χ502222-2-2-2-2222-2-22i2i−2i−2i00000000000000-2-2-2-22222-2-2-222−2i−2i2i2i00000000000000
χ512222-2-2-2-2222-2-2−2i−2i2i2i00000000000000-2-2-2-22222-2-2-2222i2i−2i−2i00000000000000
χ522222-2-2-2-2-22-222000000000200-200000-2-2-2-222222-22-2-2000000000-200200000
χ532222-2-2-2-2-22-222000000000-200200000-2-2-2-222222-22-2-2000000000200-200000
χ5444-4-44-4000000000002-22-20000000000-4-444-4400000000000-22-220000000000
χ5544-4-44-400000000000-22-220000000000-4-444-44000000000002-22-20000000000
χ5644-4-4-44000000000002-2-220000000000-4-4444-400000000000-222-20000000000
χ5744-4-4-4400000000000-222-20000000000-4-4444-4000000000002-2-220000000000
χ584-44-4004i−4i000002ζ−2ζ2ζ3−2ζ300000000000000-44-4400−4i4i00000−2ζ2ζ−2ζ32ζ300000000000000
χ594-44-4004i−4i00000−2ζ2ζ−2ζ32ζ300000000000000-44-4400−4i4i000002ζ−2ζ2ζ3−2ζ300000000000000
χ604-44-400−4i4i000002ζ3−2ζ32ζ−2ζ00000000000000-44-44004i−4i00000−2ζ32ζ3−2ζ2ζ00000000000000
χ614-44-400−4i4i00000−2ζ32ζ3−2ζ2ζ00000000000000-44-44004i−4i000002ζ3−2ζ32ζ−2ζ00000000000000
χ628-8-88000000000000000000000000000-888-8000000000000000000000000000

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