Finite Group Databasebeta

← Group #134341

Character table — Group #134341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−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
χ91111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2222222-2-222-2-222-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-22222-2-222-2-222-2-222-2-20000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-222220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2220000000000000000000000000000
χ2122-22-22-2-2-2-22222-2-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000002ζ−2ζ002ζ3−2ζ3
χ2222-22-22-2-2-2-22222-2-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000−2ζ2ζ00−2ζ32ζ3
χ2322-22-22-2-2-2-22222-2-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002ζ3−2ζ3002ζ−2ζ
χ2422-22-22-2-2-2-22222-2-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ32ζ300−2ζ2ζ
χ2522-22-22-2-2-2-222-2-22200002i−2i−2i2i2i−2i−2i2i000000000000000000000000002ζ−2ζ002ζ3−2ζ300
χ2622-22-22-2-2-2-222-2-22200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000−2ζ2ζ00−2ζ32ζ300
χ2722-22-22-2-2-2-222-2-2220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000002ζ3−2ζ3002ζ−2ζ00
χ2822-22-22-2-2-2-222-2-2220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000−2ζ32ζ300−2ζ2ζ00
χ292-222-2-2-222-22-22-22-200002222-2-2-2-2000000000022-2-2002-20000000000000000
χ302-222-2-2-222-22-22-22-200002222-2-2-2-20000000000-2-22200-220000000000000000
χ312-222-2-2-222-22-22-22-20000-2-2-2-22222000000000022-2-200-220000000000000000
χ322-222-2-2-222-22-22-22-20000-2-2-2-222220000000000-2-222002-20000000000000000
χ332-222-2-2-222-22-2-22-22000022-2-2-2-2220000002i2i−2i−2i00002i−2i000000000000000000
χ342-222-2-2-222-22-2-22-22000022-2-2-2-222000000−2i−2i2i2i0000−2i2i000000000000000000
χ352-222-2-2-222-22-2-22-220000-2-22222-2-20000002i2i−2i−2i0000−2i2i000000000000000000
χ362-222-2-2-222-22-2-22-220000-2-22222-2-2000000−2i−2i2i2i00002i−2i000000000000000000
χ372-2-222-22-2-222-22-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000002ζ3−2ζ3002ζ−2ζ0000000000
χ382-2-222-22-2-222-22-2-2200002i−2i2i−2i−2i2i−2i2i000000000000000000−2ζ32ζ300−2ζ2ζ0000000000
χ392-2-222-22-2-222-22-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000002ζ−2ζ002ζ3−2ζ30000000000
χ402-2-222-22-2-222-22-2-220000−2i2i−2i2i2i−2i2i−2i000000000000000000−2ζ2ζ00−2ζ32ζ30000000000
χ412-2-222-22-2-222-2-222-200002i−2i−2i2i−2i2i2i−2i000000000000000000002ζ3−2ζ3002ζ−2ζ00000000
χ422-2-222-22-2-222-2-222-200002i−2i−2i2i−2i2i2i−2i00000000000000000000−2ζ32ζ300−2ζ2ζ00000000
χ432-2-222-22-2-222-2-222-20000−2i2i2i−2i2i−2i−2i2i000000000000000000002ζ−2ζ002ζ3−2ζ300000000
χ442-2-222-22-2-222-2-222-20000−2i2i2i−2i2i−2i−2i2i00000000000000000000−2ζ2ζ00−2ζ32ζ300000000
χ4544444444-4-4-4-4000044-4-4000000000000000000000000000000000000000000
χ4644444444-4-4-4-40000-4-444000000000000000000000000000000000000000000
χ47444-44-4-4-400000000004-4000000000000002-22-22-22-200000000000000000000
χ48444-44-4-4-400000000004-400000000000000-22-22-22-2200000000000000000000
χ49444-44-4-4-40000000000-44000000000000002-22-2-22-2200000000000000000000
χ50444-44-4-4-40000000000-4400000000000000-22-222-22-200000000000000000000
χ5144-44-44-4-444-4-40000000000000000004-4000000000000000000000000000000
χ5244-44-44-4-444-4-4000000000000000000-44000000000000000000000000000000
χ534-444-4-4-44-44-44000000000000000000004i−4i0000000000000000000000000000
χ544-444-4-4-44-44-4400000000000000000000−4i4i0000000000000000000000000000
χ554-44-4-444-4000000004i−4i00000000000000002i−2i−2i2i2-2-2200000000000000000000
χ564-44-4-444-4000000004i−4i0000000000000000−2i2i2i−2i-222-200000000000000000000
χ574-44-4-444-400000000−4i4i00000000000000002i−2i−2i2i-222-200000000000000000000
χ584-44-4-444-400000000−4i4i0000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ594-4-444-44-44-4-4400000000000000004i−4i00000000000000000000000000000000
χ604-4-444-44-44-4-440000000000000000−4i4i00000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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