Finite Group Databasebeta

← Group #129481

Character table — Group #129481

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12224444224422444444444444442244444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222222222-2-2-2-20000-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-222220000-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000022-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200002222-2-2000000000000000000000000
χ212222-2-2-2-222-2-222-2-2000022-2-222-2-222-2-20000000000002-20000000000000000
χ222222-2-2-2-222-2-222-2-2000022-2-222-2-2-2-222000000000000-220000000000000000
χ232222-2-2-2-222-2-222-2-20000-2-222-2-22222-2-2000000000000-220000000000000000
χ242222-2-2-2-222-2-222-2-20000-2-222-2-222-2-2220000000000002-20000000000000000
χ252222-2-2-2-222-2-2-2-222000022-2-2-2-222000000000022-2-22-2000000000000000000
χ262222-2-2-2-222-2-2-2-222000022-2-2-2-2220000000000-2-222-22000000000000000000
χ272222-2-2-2-222-2-2-2-2220000-2-22222-2-2000000000022-2-2-22000000000000000000
χ282222-2-2-2-222-2-2-2-2220000-2-22222-2-20000000000-2-2222-2000000000000000000
χ2922-2-222-2-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000002ζ−2ζ002ζ3−2ζ3
χ3022-2-222-2-22-22-22-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000−2ζ2ζ00−2ζ32ζ3
χ3122-2-222-2-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002ζ3−2ζ3002ζ−2ζ
χ3222-2-222-2-22-22-22-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ32ζ300−2ζ2ζ
χ3322-2-222-2-22-22-2-22-2200002i−2i2i−2i−2i2i−2i2i000000000000000000000000002ζ−2ζ002ζ3−2ζ300
χ3422-2-222-2-22-22-2-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000−2ζ2ζ00−2ζ32ζ300
χ3522-2-222-2-22-22-2-22-220000−2i2i−2i2i2i−2i2i−2i000000000000000000000000002ζ3−2ζ3002ζ−2ζ00
χ3622-2-222-2-22-22-2-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000−2ζ32ζ300−2ζ2ζ00
χ3722-2-2-2-2222-2-222-2-2200002i−2i−2i2i2i−2i−2i2i000000000000000000002ζ3−2ζ3002ζ−2ζ00000000
χ3822-2-2-2-2222-2-222-2-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000−2ζ32ζ300−2ζ2ζ00000000
χ3922-2-2-2-2222-2-222-2-220000−2i2i2i−2i−2i2i2i−2i000000000000000000002ζ−2ζ002ζ3−2ζ300000000
χ4022-2-2-2-2222-2-222-2-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000−2ζ2ζ00−2ζ32ζ300000000
χ4122-2-2-2-2222-2-22-222-200002i−2i−2i2i−2i2i2i−2i0000000000000000002ζ−2ζ002ζ3−2ζ30000000000
χ4222-2-2-2-2222-2-22-222-200002i−2i−2i2i−2i2i2i−2i000000000000000000−2ζ2ζ00−2ζ32ζ30000000000
χ4322-2-2-2-2222-2-22-222-20000−2i2i2i−2i2i−2i−2i2i0000000000000000002ζ3−2ζ3002ζ−2ζ0000000000
χ4422-2-2-2-2222-2-22-222-20000−2i2i2i−2i2i−2i−2i2i000000000000000000−2ζ32ζ300−2ζ2ζ0000000000
χ4544444444-4-4-4-4000000000000000000004i−4i0000000000000000000000000000
χ4644444444-4-4-4-400000000000000000000−4i4i0000000000000000000000000000
χ474444-4-4-4-4-4-44400004i4i−4i−4i000000000000000000000000000000000000000000
χ484444-4-4-4-4-4-4440000−4i−4i4i4i000000000000000000000000000000000000000000
χ4944-4-444-4-4-44-4400000000000000000000004i−4i00000000000000000000000000
χ5044-4-444-4-4-44-440000000000000000000000−4i4i00000000000000000000000000
χ5144-4-4-4-444-444-40000000000000000000000004i−4i000000000000000000000000
χ5244-4-4-4-444-444-4000000000000000000000000−4i4i000000000000000000000000
χ534-44-44i−4i4i−4i000000002+2i−2−2i2−2i−2+2i000000002-22i−2i0000002-22i−2i00000000000000000000
χ544-44-44i−4i4i−4i000000002+2i−2−2i2−2i−2+2i00000000-22−2i2i000000-22−2i2i00000000000000000000
χ554-44-44i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i000000002-22i−2i000000-22−2i2i00000000000000000000
χ564-44-44i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i00000000-22−2i2i0000002-22i−2i00000000000000000000
χ574-44-4−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i000000002-2−2i2i0000002-2−2i2i00000000000000000000
χ584-44-4−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i00000000-222i−2i000000-222i−2i00000000000000000000
χ594-44-4−4i4i−4i4i00000000−2+2i2−2i−2−2i2+2i000000002-2−2i2i000000-222i−2i00000000000000000000
χ604-44-4−4i4i−4i4i00000000−2+2i2−2i−2−2i2+2i00000000-222i−2i0000002-2−2i2i00000000000000000000
χ618-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000

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