Finite Group Databasebeta

← Group #13165802

Character table — Group #13165802

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222266888899991616161618181818181818182424242436363636363636363636363636363636545454545454108108108108
order1222366644366622223666444466661212121244441212121212121212121212124444444444
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ41111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ511111111-1-111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ711111111-1-1111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ811111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111
χ911-1-111-1-1i−i11-1-111-1-111-1-111-1-1-1-111ii−i−i1-11-111-1-111-1-111-1-1i−iii−i−ii−ii−i
χ1011-1-111-1-1i−i11-1-111-1-111-1-111-1-1-1-111ii−i−i-11-11-1-11111-1-1-1-111i−iii−i−i−ii−ii
χ1111-1-111-1-1i−i11-1-111-1-111-1-1-1-111-1-111ii−i−i1-1-1111-1-1-1-111-1-111i−i−i−iii−iii−i
χ1211-1-111-1-1i−i11-1-111-1-111-1-1-1-111-1-111ii−i−i-111-1-1-111-1-11111-1-1i−i−i−iiii−i−ii
χ1311-1-111-1-1−ii11-1-111-1-111-1-111-1-1-1-111−i−iii1-11-111-1-111-1-111-1-1−ii−i−iii−ii−ii
χ1411-1-111-1-1−ii11-1-111-1-111-1-111-1-1-1-111−i−iii-11-11-1-11111-1-1-1-111−ii−i−iiii−ii−i
χ1511-1-111-1-1−ii11-1-111-1-111-1-1-1-111-1-111−i−iii1-1-1111-1-1-1-111-1-111−iiii−i−ii−i−ii
χ1611-1-111-1-1−ii11-1-111-1-111-1-1-1-111-1-111−i−iii-111-1-1-111-1-11111-1-1−iiii−i−i−iii−i
χ1722222222222222-2-2-2-222220000-2-2-2-222220000000000000000-2-200000000
χ1822222222-2-22222-2-2-2-222220000-2-2-2-2-2-2-2-200000000000000002200000000
χ192222-1-1-1-10022222222-1-1-1-12222-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ202222-1-1-1-10022222222-1-1-1-12222-1-1-1-10000-2-2-2-21111-1-1-1-111110000000000
χ212222-1-1-1-10022222222-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-1-1-1-1111111110000000000
χ222222-1-1-1-10022222222-1-1-1-1-2-2-2-2-1-1-1-10000-2-22211111111-1-1-1-10000000000
χ2322-2-222-2-22i−2i22-2-2-2-22222-2-2000022-2-22i2i−2i−2i0000000000000000−2i2i00000000
χ2422-2-222-2-2−2i2i22-2-2-2-22222-2-2000022-2-2−2i−2i2i2i00000000000000002i−2i00000000
χ2522-2-2-1-1110022-2-222-2-2-1-11122-2-211-1-100002-22-2-1-111-1-111-1-1110000000000
χ2622-2-2-1-1110022-2-222-2-2-1-11122-2-211-1-10000-22-2211-1-1-1-11111-1-10000000000
χ2722-2-2-1-1110022-2-222-2-2-1-111-2-22211-1-100002-2-22-1-11111-1-111-1-10000000000
χ2822-2-2-1-1110022-2-222-2-2-1-111-2-22211-1-10000-222-211-1-111-1-1-1-1110000000000
χ292-22-22-22-2002-22-22-2-222-22-22i−2i2i−2i2-22-20000000000002i−2i2i−2i00000000000000
χ302-22-22-22-2002-22-22-2-222-22-2−2i2i−2i2i2-22-2000000000000−2i2i−2i2i00000000000000
χ312-22-22-22-2002-22-2-222-22-22-20000-22-2200000000000000000000002i−2i2i−2i0000
χ322-22-22-22-2002-22-2-222-22-22-20000-22-220000000000000000000000−2i2i−2i2i0000
χ332-22-2-11-11002-22-22-2-22-11-112i−2i2i−2i-11-1100000000−i3i3−i3i3−ii−ii3−33−30000000000
χ342-22-2-11-11002-22-22-2-22-11-112i−2i2i−2i-11-1100000000i3−i3i3−i3−ii−ii−33−330000000000
χ352-22-2-11-11002-22-22-2-22-11-11−2i2i−2i2i-11-1100000000−i3i3−i3i3i−ii−i−33−330000000000
χ362-22-2-11-11002-22-22-2-22-11-11−2i2i−2i2i-11-1100000000i3−i3i3−i3i−ii−i3−33−30000000000
χ372-2-222-2-22002-2-222-22-22-2-222i−2i−2i2i-222-20000000000002i−2i−2i2i00000000000000
χ382-2-222-2-22002-2-222-22-22-2-22−2i2i2i−2i-222-2000000000000−2i2i2i−2i00000000000000
χ392-2-222-2-22002-2-22-22-222-2-2200002-2-2200000000000000000000002-2-220000
χ402-2-222-2-22002-2-22-22-222-2-2200002-2-220000000000000000000000-222-20000
χ412-2-22-111-1002-2-222-22-2-111-12i−2i−2i2i1-1-1100000000−i3i3i3−i3−iii−i3−3−330000000000
χ422-2-22-111-1002-2-222-22-2-111-12i−2i−2i2i1-1-1100000000i3−i3−i3i3−iii−i−333−30000000000
χ432-2-22-111-1002-2-222-22-2-111-1−2i2i2i−2i1-1-1100000000−i3i3i3−i3i−i−ii−333−30000000000
χ442-2-22-111-1002-2-222-22-2-111-1−2i2i2i−2i1-1-1100000000i3−i3−i3i3i−i−ii3−3−330000000000
χ454444-2-2-2-2004444-4-4-4-4-2-2-2-200002222000000000000000000000000000000
χ4644-4-4-2-2220044-4-4-4-444-2-2220000-2-222000000000000000000000000000000
χ474-44-4-22-22004-44-4-444-4-22-2200002-22-2000000000000000000000000000000
χ484-4-44-222-2004-4-44-44-44-222-20000-222-2000000000000000000000000000000
χ498888888888-1-1-1-10000-1-1-1-100000000-1-1-1-100000000000000000000000000
χ5088888888-8-8-1-1-1-10000-1-1-1-100000000111100000000000000000000000000
χ5188-8-888-8-88i−8i-1-1110000-1-11100000000−i−iii00000000000000000000000000
χ5288-8-888-8-8−8i8i-1-1110000-1-11100000000ii−i−i00000000000000000000000000
χ538-88-88-88-800-11-110000-11-11000000003i−3i3i−3i00000000000000000000000000
χ548-88-88-88-800-11-110000-11-1100000000−3i3i−3i3i00000000000000000000000000
χ558-8-888-8-8800-111-10000-111-1000000003-3-3300000000000000000000000000
χ568-8-888-8-8800-111-10000-111-100000000-333-300000000000000000000000000
χ5716161616-8-8-8-800-2-2-2-20000111100000000000000000000000000000000000000
χ581616-16-16-8-88800-2-222000011-1-100000000000000000000000000000000000000
χ5916-1616-16-88-8800-22-2200001-11-100000000000000000000000000000000000000
χ6016-16-1616-888-800-222-200001-1-1100000000000000000000000000000000000000

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