Finite Group Databasebeta

← Group #239371

Character table — Group #239371

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222224444444444444444888888888888888822444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1111-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-11-1-1-1111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-11111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1-11-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-111-11111-1-1-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111-1-11-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-111-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-11-1-1-111-1-11111-1-1-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11-1111-1-1-1-111-1-11111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-11-1-1-11111-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-11-1111-1-111-1-111-1-1-1-111
χ172222222222-2-222-2-2-2-2-2-2222-2-2-20000000000000000000000002-22-200000000
χ182222222222-2-222-2-2-2-2-2-2222-2-2-2000000000000000000000000-22-2200000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-22220000000000000000000000002-2-2200000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2222000000000000000000000000-222-200000000
χ2122222-2-2-22-2222222-2-22-22-2-22-2-2000000000000000000000000000000002i−2i2i−2i
χ2222222-2-2-22-2222222-2-22-22-2-22-2-200000000000000000000000000000000−2i2i−2i2i
χ2322222-2-2-22-222-2-2-2-2-2-22-2-222-222000000000000000000000000000000002i−2i−2i2i
χ2422222-2-2-22-222-2-2-2-2-2-22-2-222-22200000000000000000000000000000000−2i2i2i−2i
χ2522222-2-2-22-2-2-222-2-222-222-2-2-222000000000000000020-22-2000000000000000
χ2622222-2-2-22-2-2-222-2-222-222-2-2-2220000000000000000-202-22000000000000000
χ2722222-2-2-22-2-2-2-2-22222-22-2222-2-2000000000000000020-2-22000000000000000
χ2822222-2-2-22-2-2-2-2-22222-22-2222-2-20000000000000000-2022-2000000000000000
χ292222-22-2-2-22222222-2-2-22-22-2-22-200000000000000000000000000002i−2i2i−2i0000
χ302222-22-2-2-22222222-2-2-22-22-2-22-20000000000000000000000000000−2i2i−2i2i0000
χ312222-22-2-2-2222-2-2-2-2-2-2-222-222-2200000000000000000000000000002i−2i−2i2i0000
χ322222-22-2-2-2222-2-2-2-2-2-2-222-222-220000000000000000000000000000−2i2i2i−2i0000
χ332222-22-2-2-22-2-222-2-2222-2-22-22-22000000000000000002000-22-2000000000000
χ342222-22-2-2-22-2-222-2-2222-2-22-22-2200000000000000000-20002-22000000000000
χ352222-22-2-2-22-2-2-2-222222-22-22-22-2000000000000000002000-2-22000000000000
χ362222-22-2-2-22-2-2-2-222222-22-22-22-200000000000000000-200022-2000000000000
χ372222-2-222-2-222222222-2-2-2-22-2-2222-2-2-2-2220000000000000000000000000000
χ382222-2-222-2-222222222-2-2-2-22-2-22-2-22222-2-20000000000000000000000000000
χ392222-2-222-2-222-2-2-2-222-2-222-222-22222-2-2-2-20000000000000000000000000000
χ402222-2-222-2-222-2-2-2-222-2-222-222-2-2-2-2-222220000000000000000000000000000
χ412222-2-222-2-2-2-222-2-2-2-222-2-2222-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ422222-2-222-2-2-2-222-2-2-2-222-2-2222-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ432222-2-222-2-2-2-2-2-222-2-22222-2-2-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ442222-2-222-2-2-2-2-2-222-2-22222-2-2-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4544-4-40000004i−4i4-44i−4i0000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000000000000000
χ4644-4-40000004i−4i4-44i−4i000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000000000000000
χ4744-4-40000004i−4i-44−4i4i0000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000000000000000
χ4844-4-40000004i−4i-44−4i4i000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ300000000000000000000
χ4944-4-4000000−4i4i4-4−4i4i0000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000
χ5044-4-4000000−4i4i4-4−4i4i000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5144-4-4000000−4i4i-444i−4i0000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5244-4-4000000−4i4i-444i−4i000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ00000000000000000000
χ534-44-4444-4-4-4000000000000000022−220022−22000000000000000000000000000000
χ544-44-4444-4-4-40000000000000000−222200−2222000000000000000000000000000000
χ554-44-44-4-44-440000000000000000002i2−2i2002i2−2i20000000000000000000000000000
χ564-44-44-4-44-44000000000000000000−2i22i200−2i22i20000000000000000000000000000
χ574-44-4-44-444-40000000000000000002i2−2i200−2i22i20000000000000000000000000000
χ584-44-4-44-444-4000000000000000000−2i22i2002i2−2i20000000000000000000000000000
χ594-44-4-4-44-444000000000000000022−2200−2222000000000000000000000000000000
χ604-44-4-4-44-4440000000000000000−22220022−22000000000000000000000000000000
χ618-8-880000000000008-800000000000000000000000000000000000000000000
χ628-8-88000000000000-8800000000000000000000000000000000000000000000

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