Finite Group Databasebeta

← Group #136458

Character table — Group #136458

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order122244444444244488888888244488881616161616161616161616161616161688888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1
χ91111-1-1-1-1-1-111-111-1-1-1-1-1111111-1-1ii−i−i1111-1-1-1-11111-1-1-1-1i−ii−ii−i1-1ii−i−ii−i
χ101111-1-1-1-1-1-111-111-1-1-1-1-1111111-1-1ii−i−i-1-1-1-11111-1-1-1-11111i−ii−ii−i1-1−i−iii−ii
χ111111-1-1-1-1-1-111-111-1-1-1-1-1111111-1-1−i−iii1111-1-1-1-11111-1-1-1-1−ii−ii−ii1-1−i−iii−ii
χ121111-1-1-1-1-1-111-111-1-1-1-1-1111111-1-1−i−iii-1-1-1-11111-1-1-1-11111−ii−ii−ii1-1ii−i−ii−i
χ131111-1-1-1-1-1-111-111-1-1-1-1-11111-1-111ii−i−i1111-1-1-1-1-1-1-1-11111−iii−i−ii-11ii−i−i−ii
χ141111-1-1-1-1-1-111-111-1-1-1-1-11111-1-111ii−i−i-1-1-1-111111111-1-1-1-1−iii−i−ii-11−i−iiii−i
χ151111-1-1-1-1-1-111-111-1-1-1-1-11111-1-111−i−iii1111-1-1-1-1-1-1-1-11111i−i−iii−i-11−i−iiii−i
χ161111-1-1-1-1-1-111-111-1-1-1-1-11111-1-111−i−iii-1-1-1-111111111-1-1-1-1i−i−iii−i-11ii−i−i−ii
χ172222222222222222-2-2-2-2-2-2-2-2222200000000000000000000000000-2-2000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000022000000
χ19222222222222-2-2-2-222-2-222-2-20000000000000000000000002200-2-200000000
χ20222222222222-2-2-2-222-2-222-2-2000000000000000000000000-2-2002200000000
χ21222222222222-2-2-2-2-2-222-2-22200002222000000000000000000-2-20000000000
χ22222222222222-2-2-2-2-2-222-2-2220000-2-2-2-2000000000000000000220000000000
χ2322222222-2-2-2-2-22-22000000002-22-2000022−2−222−2−222−2−222−2−200000000000000
χ2422222222-2-2-2-2-22-22000000002-22-20000−2−222−2−222−2−222−2−22200000000000000
χ2522222222-2-2-2-2-22-2200000000-22-22000022−2−222−2−2−2−222−2−22200000000000000
χ2622222222-2-2-2-2-22-2200000000-22-220000−2−222−2−22222−2−222−2−200000000000000
χ272222-2-2-2-222-2-222-2-2000000002-2-22000022−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-2-2-222-2-222-2-2000000002-2-220000−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-2-2-222-2-222-2-200000000-222-2000022−2−2−2−222−2−22222−2−200000000000000
χ302222-2-2-2-222-2-222-2-200000000-222-20000−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-2-2-2222-2-2222-2-2-2-22200002i2i−2i−2i000000000000000000−2i2i0000000000
χ322222-2-2-2-2-2-2222-2-2222-2-2-2-2220000−2i−2i2i2i0000000000000000002i−2i0000000000
χ332222-2-2-2-2-2-2222-2-22-2-22222-2-20000000000000000000000002i−2i00−2i2i00000000
χ342222-2-2-2-2-2-2222-2-22-2-22222-2-2000000000000000000000000−2i2i002i−2i00000000
χ352222-2-2-2-2-2-222-222-22222-2-2-2-222-2-200000000000000000000000000-22000000
χ362222-2-2-2-2-2-222-222-22222-2-2-2-2-2-222000000000000000000000000002-2000000
χ3722-2-22i−2i2i−2i2i−2i2-20000002i−2i002-200002ζ2−2ζ22ζ6−2ζ6i2−i2i2−i22−22−200000000000000001−i−1+i1+i−1−i00
χ3822-2-22i−2i2i−2i2i−2i2-20000002i−2i002-200002ζ2−2ζ22ζ6−2ζ6−i2i2−i2i2−22−220000000000000000−1+i1−i−1−i1+i00
χ3922-2-22i−2i2i−2i2i−2i2-20000002i−2i002-20000−2ζ22ζ2−2ζ62ζ6i2−i2i2−i22−22−20000000000000000−1+i1−i−1−i1+i00
χ4022-2-22i−2i2i−2i2i−2i2-20000002i−2i002-20000−2ζ22ζ2−2ζ62ζ6−i2i2−i2i2−22−2200000000000000001−i−1+i1+i−1−i00
χ4122-2-2−2i2i−2i2i−2i2i2-2000000−2i2i002-200002ζ6−2ζ62ζ2−2ζ2i2−i2i2−i2−22−2200000000000000001+i−1−i1−i−1+i00
χ4222-2-2−2i2i−2i2i−2i2i2-2000000−2i2i002-200002ζ6−2ζ62ζ2−2ζ2−i2i2−i2i22−22−20000000000000000−1−i1+i−1+i1−i00
χ4322-2-2−2i2i−2i2i−2i2i2-2000000−2i2i002-20000−2ζ62ζ6−2ζ22ζ2i2−i2i2−i2−22−220000000000000000−1−i1+i−1+i1−i00
χ4422-2-2−2i2i−2i2i−2i2i2-2000000−2i2i002-20000−2ζ62ζ6−2ζ22ζ2−i2i2−i2i22−22−200000000000000001+i−1−i1−i−1+i00
χ4544444444-4-4-4-44-44-40000000000000000000000000000000000000000000000
χ464444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000000000
χ4744-4-44i−4i4i−4i4i−4i4-4000000−4i4i00-4400000000000000000000000000000000000000
χ4844-4-44i−4i4i−4i−4i4i-44000000000000000000002i−2i−2i2i2-2-220000000000000000000000
χ4944-4-44i−4i4i−4i−4i4i-4400000000000000000000−2i2i2i−2i-222-20000000000000000000000
χ5044-4-4−4i4i−4i4i4i−4i-44000000000000000000002i−2i−2i2i-222-20000000000000000000000
χ5144-4-4−4i4i−4i4i4i−4i-4400000000000000000000−2i2i2i−2i2-2-220000000000000000000000
χ5244-4-4−4i4i−4i4i−4i4i4-40000004i−4i00-4400000000000000000000000000000000000000
χ534-44-444-4-40000000022−220022−22000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ544-44-444-4-40000000022−220022−22000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ554-44-444-4-400000000−222200−2222000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ564-44-444-4-400000000−222200−2222000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ574-44-4-4-4440000000022−2200−2222000000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ584-44-4-4-4440000000022−2200−2222000000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ594-44-4-4-44400000000−22220022−22000000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ604-44-4-4-44400000000−22220022−22000000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ618-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.