Finite Group Databasebeta

← Group #317113

Character table — Group #317113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12224444224444448888888888882244444488888822444488888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-11-1-1-1111-1-1111111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1111-1-1-111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1111-11-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ121111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-111111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1111-111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-1-11-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-11111-1-1-1-111
χ17222222222222-2-2-2-222222222-2-2-2-2000022-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-222220000-2-222-2-2000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000-2-22222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-2-222000000000000000000000000
χ212222-2-2-2-222-2-22-22-22i2i−2i−2i00000000000000002i−2i2i2i−2i−2i2000-2000000000000000
χ222222-2-2-2-222-2-22-22-22i2i−2i−2i00000000000000002i−2i−2i−2i2i2i-20002000000000000000
χ232222-2-2-2-222-2-22-22-2−2i−2i2i2i0000000000000000−2i2i2i2i−2i−2i-20002000000000000000
χ242222-2-2-2-222-2-22-22-2−2i−2i2i2i0000000000000000−2i2i−2i−2i2i2i2000-2000000000000000
χ252222-2-2-2-222-2-2-22-222i2i−2i−2i0000000022-2-20000−2i2i000000000000002i−2i00000000
χ262222-2-2-2-222-2-2-22-222i2i−2i−2i00000000-2-2220000−2i2i00000000000000−2i2i00000000
χ272222-2-2-2-222-2-2-22-22−2i−2i2i2i0000000022-2-200002i−2i00000000000000−2i2i00000000
χ282222-2-2-2-222-2-2-22-22−2i−2i2i2i00000000-2-22200002i−2i000000000000002i−2i00000000
χ292222-2-2-2-2-2-22222-2-2000022-2-222-2-2000000000000000000002i−2i2i−2i0000000000
χ302222-2-2-2-2-2-22222-2-2000022-2-222-2-200000000000000000000−2i2i−2i2i0000000000
χ312222-2-2-2-2-2-22222-2-20000-2-222-2-222000000000000000000002i−2i−2i2i0000000000
χ322222-2-2-2-2-2-22222-2-20000-2-222-2-22200000000000000000000−2i2i2i−2i0000000000
χ332222-2-2-2-2-2-222-2-222000022-2-2-2-22200000000000000022-20-200000000000000
χ342222-2-2-2-2-2-222-2-222000022-2-2-2-222000000000000000-2-220200000000000000
χ352222-2-2-2-2-2-222-2-2220000-2-22222-2-20000000000000002-220-200000000000000
χ362222-2-2-2-2-2-222-2-2220000-2-22222-2-2000000000000000-22-20200000000000000
χ372-2-2222-2-22-22-200002i−2i2i−2i00002i−2i2i−2i0000002-20000000000000000002−2i2−i2i2−i22−2
χ382-2-2222-2-22-22-200002i−2i2i−2i00002i−2i2i−2i0000002-2000000000000000000−22−i2i2−i2i2−22
χ392-2-2222-2-22-22-200002i−2i2i−2i0000−2i2i−2i2i000000-220000000000000000002−2i2−i2−i2i2−22
χ402-2-2222-2-22-22-200002i−2i2i−2i0000−2i2i−2i2i000000-22000000000000000000−22−i2i2i2−i22−2
χ412-2-2222-2-22-22-20000−2i2i−2i2i00002i−2i2i−2i000000-220000000000000000002−2−i2i2i2−i2−22
χ422-2-2222-2-22-22-20000−2i2i−2i2i00002i−2i2i−2i000000-22000000000000000000−22i2−i2−i2i22−2
χ432-2-2222-2-22-22-20000−2i2i−2i2i0000−2i2i−2i2i0000002-20000000000000000002−2−i2i2−i2i22−2
χ442-2-2222-2-22-22-20000−2i2i−2i2i0000−2i2i−2i2i0000002-2000000000000000000−22i2−i2i2−i2−22
χ4544444444-4-4-4-44-4-440000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-444-40000000000000000000000000000000000000000000000
χ4744-4-44i−4i4i−4i0000000000002i2−2i222−2200002-22i−2i0000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ4844-4-44i−4i4i−4i0000000000002i2−2i222−220000-22−2i2i000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ4944-4-44i−4i4i−4i000000000000−2i22i2−222200002-22i−2i000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ5044-4-44i−4i4i−4i000000000000−2i22i2−22220000-22−2i2i0000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ5144-4-4−4i4i−4i4i0000000000002i2−2i2−222200002-2−2i2i0000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ5244-4-4−4i4i−4i4i0000000000002i2−2i2−22220000-222i−2i000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5344-4-4−4i4i−4i4i000000000000−2i22i222−2200002-2−2i2i000000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5444-4-4−4i4i−4i4i000000000000−2i22i222−220000-222i−2i0000002ζ3−2ζ32ζ−2ζ00000000000000000000
χ554-4-4444-4-4-44-44000000000000000000004-40000000000000000000000000000
χ564-4-4444-4-4-44-4400000000000000000000-440000000000000000000000000000
χ574-4-44-4-4444-4-4400004-4-44000000000000000000000000000000000000000000
χ584-4-44-4-4444-4-440000-444-4000000000000000000000000000000000000000000
χ594-4-44-4-444-444-40000000000004i−4i−4i4i0000000000000000000000000000000000
χ604-4-44-4-444-444-4000000000000−4i4i4i−4i0000000000000000000000000000000000
χ618-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000

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