Finite Group Databasebeta

← Group #239394

Character table — Group #239394

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222224444444444444444444444448888888824444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111111111-1-111-1-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-11-11-1
χ101111111111-1-111-1-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1111-11-1
χ111111111111-1-111-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-11-11
χ121111111111-1-111-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-11-11
χ131111111111-1-111-1-111-1-1-111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-11-11
χ141111111111-1-111-1-111-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111-11-11
χ151111111111-1-111-1-111-1-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-1111-11-1
χ161111111111-1-111-1-111-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-11-11-1
χ17222222222222-2-2-2-2-2-2222-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-222222-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2222-2-22222-2-20000000000000000000000000000
χ2122222-2-2-2-22222222-2-22-2-22-22-2-20000000000000000000000002i−2i2i−2i00000000
χ2222222-2-2-2-22222222-2-22-2-22-22-2-2000000000000000000000000−2i2i−2i2i00000000
χ2322222-2-2-2-2222-2-2-2-2222-2-2-22-22200000000000000002-22-20000000000000000
χ2422222-2-2-2-2222-2-2-2-2222-2-2-22-2220000000000000000-22-220000000000000000
χ2522222-2-2-2-22-2-222-2-2-2-2-2222-2-2220000000000000000000000002i−2i−2i2i00000000
χ2622222-2-2-2-22-2-222-2-2-2-2-2222-2-222000000000000000000000000−2i2i2i−2i00000000
χ2722222-2-2-2-22-2-2-2-22222-222-222-2-200000000000000002-2-220000000000000000
χ2822222-2-2-2-22-2-2-2-22222-222-222-2-20000000000000000-222-20000000000000000
χ292222-222-2-2-222222222-22-2-2-2-22-20000000000000000000000000000000022-2-2
χ302222-222-2-2-222222222-22-2-2-2-22-200000000000000000000000000000000-2-222
χ312222-222-2-2-222-2-2-2-2-2-2-22-2222-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ322222-222-2-2-222-2-2-2-2-2-2-22-2222-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ332222-222-2-2-2-2-222-2-2222-22-2-22-22000000000000000000000000000000002-2-22
χ342222-222-2-2-2-2-222-2-2222-22-2-22-2200000000000000000000000000000000-222-2
χ352222-222-2-2-2-2-2-2-222-2-22-2222-22-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ362222-222-2-2-2-2-2-2-222-2-22-2222-22-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ372222-2-2-222-2222222-2-2-2-22-22-2-2200000000000000000000000000002i−2i2i−2i0000
χ382222-2-2-222-2222222-2-2-2-22-22-2-220000000000000000000000000000−2i2i−2i2i0000
χ392222-2-2-222-222-2-2-2-222-2-222-222-2000000000000000000002-22-2000000000000
χ402222-2-2-222-222-2-2-2-222-2-222-222-200000000000000000000-22-22000000000000
χ412222-2-2-222-2-2-222-2-2-2-222-2-2222-200000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-222-2-2-222-2-2-2-222-2-2222-20000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-222-2-2-2-2-2222222-22-2-2-22000000000000000000002-2-22000000000000
χ442222-2-2-222-2-2-2-2-2222222-22-2-2-2200000000000000000000-222-2000000000000
χ4544-4-444-44-4-4000000000000000000004-4000000000000000000000000000000
χ4644-4-444-44-4-400000000000000000000-44000000000000000000000000000000
χ4744-4-44-44-44-40000000000000000004-400000000000000000000000000000000
χ4844-4-44-44-44-4000000000000000000-4400000000000000000000000000000000
χ4944-4-4-44-4-44400000000000000000000004i−4i0000000000000000000000000000
χ5044-4-4-44-4-4440000000000000000000000−4i4i0000000000000000000000000000
χ5144-4-4-4-444-4400000000000000004i−4i0000000000000000000000000000000000
χ5244-4-4-4-444-440000000000000000−4i4i0000000000000000000000000000000000
χ534-44-40000004i−4i4i−4i4-40000000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ00000000000000000000
χ544-44-40000004i−4i4i−4i4-4000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ00000000000000000000
χ554-44-40000004i−4i−4i4i-440000000000000000002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000000000000000
χ564-44-40000004i−4i−4i4i-44000000000000000000−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000000000000000
χ574-44-4000000−4i4i4i−4i-440000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ00000000000000000000
χ584-44-4000000−4i4i4i−4i-44000000000000000000−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ00000000000000000000
χ594-44-4000000−4i4i−4i4i4-40000000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ300000000000000000000
χ604-44-4000000−4i4i−4i4i4-4000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ300000000000000000000
χ618-8-880000000000008-800000000000000000000000000000000000000000000
χ628-8-88000000000000-8800000000000000000000000000000000000000000000

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