Finite Group Databasebeta

← Group #121499

Character table — Group #121499

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444442244444444444444448888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ91-1111-1-1-11111-1-1-1-11-11-1-1-1-1111ii−i−iii−i−i1111-1-1-1-1i−ii−ii−ii−iii−i−i11-1-111-1-1
χ101-1111-1-1-11111-1-1-1-11-11-1-1-1-1111ii−i−iii−i−i1111-1-1-1-1−iii−ii−i−ii−i−iii-1-111-1-111
χ111-1111-1-1-11111-1-1-1-11-11-1-1-1-1111ii−i−iii−i−i-1-1-1-11111i−i−ii−iii−i−i−iii11-1-1-1-111
χ121-1111-1-1-11111-1-1-1-11-11-1-1-1-1111ii−i−iii−i−i-1-1-1-11111−ii−ii−ii−iiii−i−i-1-11111-1-1
χ131-1111-1-1-11111-1-1-1-11-11-1-1-1-1111−i−iii−i−iii1111-1-1-1-1i−i−ii−iii−iii−i−i-1-111-1-111
χ141-1111-1-1-11111-1-1-1-11-11-1-1-1-1111−i−iii−i−iii1111-1-1-1-1−ii−ii−ii−ii−i−iii11-1-111-1-1
χ151-1111-1-1-11111-1-1-1-11-11-1-1-1-1111−i−iii−i−iii-1-1-1-11111i−ii−ii−ii−i−i−iii-1-11111-1-1
χ161-1111-1-1-11111-1-1-1-11-11-1-1-1-1111−i−iii−i−iii-1-1-1-11111−iii−ii−i−iiii−i−i11-1-1-1-111
χ172222222222222222-2-2-22-2-2-22-2-20000000022-2-222-2-200000000000000000000
χ182222222222222222-2-2-22-2-2-22-2-200000000-2-222-2-22200000000000000000000
χ192222222222-2-222-2-2222-22-2-2-2-2-20000000000000000000000002i−2i2i−2i00000000
χ202222222222-2-222-2-2222-22-2-2-2-2-2000000000000000000000000−2i2i−2i2i00000000
χ212222222222-2-222-2-2-2-2-2-2-222-2220000000000000000220000-2-2000000000000
χ222222222222-2-222-2-2-2-2-2-2-222-2220000000000000000-2-2000022000000000000
χ2322222222-2-222-2-22222-2-2-22-2-22-2000000000000000000000000000000002-22-2
χ2422222222-2-222-2-22222-2-2-22-2-22-200000000000000000000000000000000-22-22
χ2522222222-2-222-2-222-2-22-22-22-2-2200000000000000000000000000002-22-20000
χ2622222222-2-222-2-222-2-22-22-22-2-220000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-2-2-222-22-2-222-222222-2-2-2-20000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-22-2-222-22-2-2-2-222220000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-2-22222-222-200000000000000000022-2-200000000000000
χ3022222222-2-2-2-2-2-2-2-2-2-22222-222-2000000000000000000-2-22200000000000000
χ312-2222-2-2-22222-2-2-2-2-22-2-22222-2-20000000022-2-2-2-22200000000000000000000
χ322-2222-2-2-22222-2-2-2-2-22-2-22222-2-200000000-2-22222-2-200000000000000000000
χ332-2222-2-2-222-2-2-2-2222-222-222-2-2-20000000000000000000000002-2-2200000000
χ342-2222-2-2-222-2-2-2-2222-222-222-2-2-2000000000000000000000000-222-200000000
χ352-2222-2-2-222-2-2-2-222-22-222-2-2-22200000000000000002i−2i0000−2i2i000000000000
χ362-2222-2-2-222-2-2-2-222-22-222-2-2-2220000000000000000−2i2i00002i−2i000000000000
χ372-2222-2-2-2-2-22222-2-22-2-222-22-22-2000000000000000000000000000000002-2-22
χ382-2222-2-2-2-2-22222-2-22-2-222-22-22-200000000000000000000000000000000-222-2
χ392-2222-2-2-2-2-22222-2-2-2222-22-2-2-2200000000000000000000000000002-2-220000
χ402-2222-2-2-2-2-22222-2-2-2222-22-2-2-220000000000000000000000000000-222-20000
χ412-2222-2-2-2-2-2-2-222222-2-2-222-22-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ422-2222-2-2-2-2-2-2-222222-2-2-222-22-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ432-2222-2-2-2-2-2-2-22222-222-2-2-2222-20000000000000000002i−2i−2i2i00000000000000
χ442-2222-2-2-2-2-2-2-22222-222-2-2-2222-2000000000000000000−2i2i2i−2i00000000000000
χ45444-4-44-4-44-4004-4000000000000000000000022−220022−2200000000000000000000
χ46444-4-44-4-44-4004-40000000000000000000000−222200−222200000000000000000000
χ47444-4-44-4-4-4400-440000000000000000000022−220022−220000000000000000000000
χ48444-4-44-4-4-4400-4400000000000000000000−222200−22220000000000000000000000
χ4944-44-4-4-44004i−4i004i−4i00000000002i−2i2i−2i2-22-20000000000000000000000000000
χ5044-44-4-4-44004i−4i004i−4i0000000000−2i2i−2i2i-22-220000000000000000000000000000
χ5144-44-4-4-4400−4i4i00−4i4i00000000002i−2i2i−2i-22-220000000000000000000000000000
χ5244-44-4-4-4400−4i4i00−4i4i0000000000−2i2i−2i2i2-22-20000000000000000000000000000
χ534-44-4-4-4444-400-44000000000000000000000022−2200−222200000000000000000000
χ544-44-4-4-4444-400-440000000000000000000000−22220022−2200000000000000000000
χ554-44-4-4-444-44004-40000000000000000000022−2200−22220000000000000000000000
χ564-44-4-4-444-44004-400000000000000000000−22220022−220000000000000000000000
χ574-4-44-444-4004i−4i00−4i4i00000000002-2-22−2i2i2i−2i0000000000000000000000000000
χ584-4-44-444-4004i−4i00−4i4i0000000000-222-22i−2i−2i2i0000000000000000000000000000
χ594-4-44-444-400−4i4i004i−4i00000000002-2-222i−2i−2i2i0000000000000000000000000000
χ604-4-44-444-400−4i4i004i−4i0000000000-222-2−2i2i2i−2i0000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).