Finite Group Databasebeta

← Group #134331

Character table — Group #134331

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
χ51111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-222-2-2-2-222-2-20000000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-2220000000000000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-20000000000000000000000000000
χ2122-2-22-2-222-22-20000222222-2-2-2-2-2-2000000000022-2-2002-20000000000000000
χ2222-2-22-2-222-22-20000222222-2-2-2-2-2-20000000000-2-22200-220000000000000000
χ2322-2-22-2-222-22-2000022-2-2-2-222-2-2220000002i2i−2i−2i00002i−2i000000000000000000
χ2422-2-22-2-222-22-2000022-2-2-2-222-2-222000000−2i−2i2i2i0000−2i2i000000000000000000
χ2522-2-22-2-222-22-20000-2-222-2-22222-2-20000002i2i−2i−2i0000−2i2i000000000000000000
χ2622-2-22-2-222-22-20000-2-222-2-22222-2-2000000−2i−2i2i2i00002i−2i000000000000000000
χ2722-2-22-2-222-22-20000-2-2-2-222-2-22222000000000022-2-200-220000000000000000
χ2822-2-22-2-222-22-20000-2-2-2-222-2-222220000000000-2-222002-20000000000000000
χ292-222-2-2-222-2-2200002i−2i2i−2i2-22-22i−2i2i−2i00000000000000000000000000002ζ3−2ζ3002ζ−2ζ
χ302-222-2-2-222-2-2200002i−2i2i−2i2-22-22i−2i2i−2i0000000000000000000000000000−2ζ32ζ300−2ζ2ζ
χ312-222-2-2-222-2-2200002i−2i−2i2i-22-222i−2i−2i2i000000000000000000000000002ζ−2ζ002ζ3−2ζ300
χ322-222-2-2-222-2-2200002i−2i−2i2i-22-222i−2i−2i2i00000000000000000000000000−2ζ2ζ00−2ζ32ζ300
χ332-222-2-2-222-2-220000−2i2i2i−2i-22-22−2i2i2i−2i000000000000000000000000002ζ3−2ζ3002ζ−2ζ00
χ342-222-2-2-222-2-220000−2i2i2i−2i-22-22−2i2i2i−2i00000000000000000000000000−2ζ32ζ300−2ζ2ζ00
χ352-222-2-2-222-2-220000−2i2i−2i2i2-22-2−2i2i−2i2i00000000000000000000000000002ζ−2ζ002ζ3−2ζ3
χ362-222-2-2-222-2-220000−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000−2ζ2ζ00−2ζ32ζ3
χ372-2-2-2-222222-2-200002i−2i2i−2i2-2-22−2i2i−2i2i0000000000000000002ζ3−2ζ3002ζ−2ζ0000000000
χ382-2-2-2-222222-2-200002i−2i2i−2i2-2-22−2i2i−2i2i000000000000000000−2ζ32ζ300−2ζ2ζ0000000000
χ392-2-2-2-222222-2-200002i−2i−2i2i-222-2−2i2i2i−2i000000000000000000002ζ−2ζ002ζ3−2ζ300000000
χ402-2-2-2-222222-2-200002i−2i−2i2i-222-2−2i2i2i−2i00000000000000000000−2ζ2ζ00−2ζ32ζ300000000
χ412-2-2-2-222222-2-20000−2i2i2i−2i-222-22i−2i−2i2i000000000000000000002ζ3−2ζ3002ζ−2ζ00000000
χ422-2-2-2-222222-2-20000−2i2i2i−2i-222-22i−2i−2i2i00000000000000000000−2ζ32ζ300−2ζ2ζ00000000
χ432-2-2-2-222222-2-20000−2i2i−2i2i2-2-222i−2i2i−2i0000000000000000002ζ−2ζ002ζ3−2ζ30000000000
χ442-2-2-2-222222-2-20000−2i2i−2i2i2-2-222i−2i2i−2i000000000000000000−2ζ2ζ00−2ζ32ζ30000000000
χ4544444444-4-4-4-444-4-40000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-4-4440000000000000000000000000000000000000000000000
χ4744-4-44-4-44-44-4400000000000000004i−4i00000000000000000000000000000000
χ4844-4-44-4-44-44-440000000000000000−4i4i00000000000000000000000000000000
χ494-444-4-4-44-444-4000000000000000000004i−4i0000000000000000000000000000
χ504-444-4-4-44-444-400000000000000000000−4i4i0000000000000000000000000000
χ514-44-444-4-40000004-40000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ524-44-444-4-40000004-4000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ534-44-444-4-4000000-440000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ544-44-444-4-4000000-44000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ554-4-444-44-400004i−4i000000000000000000002-2-222i−2i−2i2i00000000000000000000
χ564-4-444-44-400004i−4i00000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ574-4-444-44-40000−4i4i000000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ584-4-444-44-40000−4i4i00000000000000000000-222-22i−2i−2i2i00000000000000000000
χ594-4-4-4-4444-4-4440000000000000000004-4000000000000000000000000000000
χ604-4-4-4-4444-4-444000000000000000000-44000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-88-88-8-8000000000000000000000000000000000000000000000000000000

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