Finite Group Databasebeta

← Group #115461

Character table — Group #115461

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444442244444444888888888888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ91-1-11-1-11111-1-1-1-1111-1111-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i1-11-11-111-1-1ii−i−i
χ101-1-11-1-11111-1-1-1-1111-1111-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i-11−i−iii1-11-1-11-1-111−i−iii
χ111-1-11-1-11111-1-1-1-1111-1111-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii1-1−i−iii-11-111-1-1-111ii−i−i
χ121-1-11-1-11111-1-1-1-1111-1111-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii-11ii−i−i-11-11-1111-1-1−i−iii
χ131-1-11-1-11111-1-1-1-1111-1111-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1ii−i−i-11-111-1-1-111−i−iii
χ141-1-11-1-11111-1-1-1-1111-1111-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i-11−i−iii-11-11-1111-1-1ii−i−i
χ151-1-11-1-11111-1-1-1-1111-1111-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii1-11-11-111-1-1−i−iii
χ161-1-11-1-11111-1-1-1-1111-1111-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii-11ii−i−i1-11-1-11-1-111ii−i−i
χ172222222222222222-2-2-22-22-2-2-2-200000000000000000000000000002-22-20000
χ182222222222222222-2-2-22-22-2-2-2-20000000000000000000000000000-22-220000
χ192222222222-2-222-2-2222-2-2-2-2-22-2000000000000000000000000000000002-22-2
χ202222222222-2-222-2-2222-2-2-2-2-22-200000000000000000000000000000000-22-22
χ212222222222-2-222-2-2-2-2-2-22-222-220000000022-2-222-2-200000000000000000000
χ222222222222-2-222-2-2-2-2-2-22-222-2200000000-2-222-2-22200000000000000000000
χ2322222222-2-222-2-22222-2-2-2-2-22-2200000000000000002200000000-2-200000000
χ2422222222-2-222-2-22222-2-2-2-2-22-220000000000000000-2-2000000002200000000
χ2522222222-2-222-2-222-2-22-22-22-22-2000000000000000000000022-2-20000000000
χ2622222222-2-222-2-222-2-22-22-22-22-20000000000000000000000-2-2220000000000
χ2722222222-2-2-2-2-2-2-2-222-22222-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-22222-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-2-222-22-22220000000000000000002-22-200000000000000
χ3022222222-2-2-2-2-2-2-2-2-2-222-22-2222000000000000000000-22-2200000000000000
χ312-2-22-2-2222222-2-2-2-22-22-2-222-2-22000000000000000000000000000000002i−2i−2i2i
χ322-2-22-2-2222222-2-2-2-22-22-2-222-2-2200000000000000000000000000000000−2i2i2i−2i
χ332-2-22-2-2222222-2-2-2-2-22-2-222-222-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ342-2-22-2-2222222-2-2-2-2-22-2-222-222-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ352-2-22-2-22222-2-2-2-222-22-22-2-22-22200000000000000000000000000002-2-220000
χ362-2-22-2-22222-2-2-2-222-22-22-2-22-2220000000000000000000000000000-222-20000
χ372-2-22-2-222-2-22222-2-22-2-222-2-2-22222-2-2-2-2220000000000000000000000000000
χ382-2-22-2-222-2-22222-2-22-2-222-2-2-222-2-22222-2-20000000000000000000000000000
χ392-2-22-2-222-2-22222-2-2-2222-2-222-2-20000000000000000002i−2i−2i2i00000000000000
χ402-2-22-2-222-2-22222-2-2-2222-2-222-2-2000000000000000000−2i2i2i−2i00000000000000
χ412-2-22-2-222-2-2-2-222222-2-2-2-22222-200000000000000002-200000000-2200000000
χ422-2-22-2-222-2-2-2-222222-2-2-2-22222-20000000000000000-22000000002-200000000
χ432-2-22-2-222-2-2-2-22222-222-222-2-2-2200000000000000000000002-2-220000000000
χ442-2-22-2-222-2-2-2-22222-222-222-2-2-220000000000000000000000-222-20000000000
χ45444-4-4-4-44004-4004-40000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ46444-4-4-4-44004-4004-4000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ47444-4-4-4-4400-4400-440000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ48444-4-4-4-4400-4400-44000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ4944-4-44-44-44i−4i004i−4i0000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ5044-4-44-44-44i−4i004i−4i000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ5144-4-44-44-4−4i4i00−4i4i0000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ5244-4-44-44-4−4i4i00−4i4i000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ534-44-4-444-44i−4i00−4i4i0000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ0000000000000000000000000000
χ544-44-4-444-44i−4i00−4i4i000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ0000000000000000000000000000
χ554-44-4-444-4−4i4i004i−4i0000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ30000000000000000000000000000
χ564-44-4-444-4−4i4i004i−4i000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ30000000000000000000000000000
χ574-4-4-444-44004-400-440000000000000000002-2-22-222-200000000000000000000
χ584-4-4-444-44004-400-44000000000000000000-222-22-2-2200000000000000000000
χ594-4-4-444-4400-44004-40000000000000000002-22-2-22-2200000000000000000000
χ604-4-4-444-4400-44004-4000000000000000000-22-222-22-200000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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