Finite Group Databasebeta

← Group #118604

Character table — Group #118604

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444442244444444888888888888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1
χ91-11-1-111-111-1-1-1-1111-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−ii−ii−i11-1-1i−ii−iii−i−i11-1-1
χ101-11-1-111-111-1-1-1-1111-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−ii−i−ii-1-111i−i−ii−i−iii-1-111
χ111-11-1-111-111-1-1-1-1111-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−iii−i-1-111−iii−iii−i−i-1-111
χ121-11-1-111-111-1-1-1-1111-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−ii−ii11-1-1−ii−ii−i−iii11-1-1
χ131-11-1-111-111-1-1-1-1111-1111-1-1-1-11-1-1-1-11111iiii−i−i−i−i−iii−i11-1-1−iii−i−i−iii-1-111
χ141-11-1-111-111-1-1-1-1111-1111-1-1-1-11-1-1-1-11111iiii−i−i−i−i−ii−ii-1-111−ii−iiii−i−i11-1-1
χ151-11-1-111-111-1-1-1-1111-1111-1-1-1-11-1-1-1-11111−i−i−i−iiiiii−ii−i-1-111i−ii−i−i−iii11-1-1
χ161-11-1-111-111-1-1-1-1111-1111-1-1-1-11-1-1-1-11111−i−i−i−iiiiii−i−ii11-1-1i−i−iiii−i−i-1-111
χ172222222222222222-2-2-22-22-2-2-2-200000000000000000000000000002-22-20000
χ182222222222222222-2-2-22-22-2-2-2-20000000000000000000000000000-22-220000
χ192222222222-2-222-2-2222-2-2-2-2-22-2000000000000000000002-22-2000000000000
χ202222222222-2-222-2-2222-2-2-2-2-22-200000000000000000000-22-22000000000000
χ212222222222-2-222-2-2-2-2-2-22-222-22000000000000000022000000-2-20000000000
χ222222222222-2-222-2-2-2-2-2-22-222-220000000000000000-2-2000000220000000000
χ2322222222-2-222-2-22222-2-2-2-22-2-22000000000000000000000000000000002-22-2
χ2422222222-2-222-2-22222-2-2-2-22-2-2200000000000000000000000000000000-22-22
χ2522222222-2-222-2-222-2-22-22-2-222-20000000022-2-222-2-200000000000000000000
χ2622222222-2-222-2-222-2-22-22-2-222-200000000-2-222-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2222-22-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2222-22-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-2-222-222-22200000000000000000022000000-2-200000000
χ3022222222-2-2-2-2-2-2-2-2-2-222-222-222000000000000000000-2-20000002200000000
χ312-22-2-222-22222-2-2-2-22-22-2-2222-2-2000000000000000000002-2-22000000000000
χ322-22-2-222-22222-2-2-2-22-22-2-2222-2-200000000000000000000-222-2000000000000
χ332-22-2-222-22222-2-2-2-2-22-2-222-2-22200000000000000002i−2i000000−2i2i0000000000
χ342-22-2-222-22222-2-2-2-2-22-2-222-2-2220000000000000000−2i2i0000002i−2i0000000000
χ352-22-2-222-222-2-2-2-222-22-22-2-2222-200000000000000000000000000002i−2i−2i2i0000
χ362-22-2-222-222-2-2-2-222-22-22-2-2222-20000000000000000000000000000−2i2i2i−2i0000
χ372-22-2-222-2-2-22222-2-22-2-222-22-22-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ382-22-2-222-2-2-22222-2-22-2-222-22-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ392-22-2-222-2-2-22222-2-2-2222-2-2-22-220000000000000000002i−2i000000−2i2i00000000
χ402-22-2-222-2-2-22222-2-2-2222-2-2-22-22000000000000000000−2i2i0000002i−2i00000000
χ412-22-2-222-2-2-2-2-222222-2-2-2-22-2222000000000000000000000000000000002-2-22
χ422-22-2-222-2-2-2-2-222222-2-2-2-22-222200000000000000000000000000000000-222-2
χ432-22-2-222-2-2-2-2-22222-222-2222-2-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ442-22-2-222-2-2-2-2-22222-222-2222-2-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ454444-4-4-4-44-4004-4000000000000000000002-22-22-22-200000000000000000000
χ464444-4-4-4-44-4004-400000000000000000000-22-22-22-2200000000000000000000
χ474444-4-4-4-4-4400-44000000000000000000002-2-222-2-2200000000000000000000
χ484444-4-4-4-4-4400-4400000000000000000000-222-2-222-200000000000000000000
χ4944-4-4-44-44004i−4i004i−4i00000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ5044-4-4-44-44004i−4i004i−4i0000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ5144-4-4-44-4400−4i4i00−4i4i00000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ5244-4-4-44-4400−4i4i00−4i4i0000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ534-44-44-4-444-400-44000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ544-44-44-4-444-400-4400000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ554-44-44-4-44-44004-4000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ564-44-44-4-44-44004-400000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ574-4-4444-4-4004i−4i00−4i4i00000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ584-4-4444-4-4004i−4i00−4i4i0000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ594-4-4444-4-400−4i4i004i−4i00000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ604-4-4444-4-400−4i4i004i−4i0000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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