Finite Group Databasebeta

← Group #13165798

Character table — Group #13165798

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222266888899991616161618181818181818182424242436363636363636363636363636363636545454545454108108108108
order1222366644366622223666444466661212121244441212121212121212121212124444444444
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ511111111-1-111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ811111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ91-1-1111-1-11-11-1-1111-1-111-1-111-1-111-1-111-1-1i−ii−i11-1-1ii−i−iii−i−i1-111-1-1i−ii−i
χ101-1-1111-1-11-11-1-1111-1-111-1-111-1-111-1-111-1-1−ii−ii11-1-1−i−iii−i−iii1-111-1-1−ii−ii
χ111-1-1111-1-11-11-1-1111-1-111-1-1-1-11111-1-111-1-1i−i−ii-1-111ii−i−i−i−iii1-1-1-111i−i−ii
χ121-1-1111-1-11-11-1-1111-1-111-1-1-1-11111-1-111-1-1−iii−i-1-111−i−iiiii−i−i1-1-1-111−iii−i
χ131-1-1111-1-1-111-1-1111-1-111-1-111-1-111-1-1-1-111i−ii−i11-1-1ii−i−iii−i−i-11-1-111−ii−ii
χ141-1-1111-1-1-111-1-1111-1-111-1-111-1-111-1-1-1-111−ii−ii11-1-1−i−iii−i−iii-11-1-111i−ii−i
χ151-1-1111-1-1-111-1-1111-1-111-1-1-1-11111-1-1-1-111i−i−ii-1-111ii−i−i−i−iii-1111-1-1−iii−i
χ161-1-1111-1-1-111-1-1111-1-111-1-1-1-11111-1-1-1-111−iii−i-1-111−i−iiiii−i−i-1111-1-1i−i−ii
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
χ202222-1-1-1-10022222222-1-1-1-12222-1-1-1-10000-2-2-2-2-1-1-1-1111111110000000000
χ212222-1-1-1-10022222222-1-1-1-1-2-2-2-2-1-1-1-1000022-2-21111-1-1-1-111110000000000
χ222222-1-1-1-10022222222-1-1-1-1-2-2-2-2-1-1-1-10000-2-22211111111-1-1-1-10000000000
χ2322-2-22-22-20022-2-22-22-22-22-20000-222-200000000000000000000002i−2i2i−2i0000
χ2422-2-22-22-20022-2-22-22-22-22-20000-222-20000000000000000000000−2i2i−2i2i0000
χ2522-2-22-22-20022-2-2-22-222-22-22i−2i2i−2i2-2-22000000002i−2i2i−2i000000000000000000
χ2622-2-22-22-20022-2-2-22-222-22-2−2i2i−2i2i2-2-2200000000−2i2i−2i2i000000000000000000
χ2722-2-2-11-110022-2-2-22-22-11-112i−2i2i−2i-111-100000000−ii−ii3−33−3−i3i3−i3i30000000000
χ2822-2-2-11-110022-2-2-22-22-11-112i−2i2i−2i-111-100000000−ii−ii−33−33i3−i3i3−i30000000000
χ2922-2-2-11-110022-2-2-22-22-11-11−2i2i−2i2i-111-100000000i−ii−i3−33−3i3−i3i3−i30000000000
χ3022-2-2-11-110022-2-2-22-22-11-11−2i2i−2i2i-111-100000000i−ii−i−33−33−i3i3−i3i30000000000
χ312-22-22-2-22002-22-22-2-222-2-220000-22-2200000000000000000000002i−2i−2i2i0000
χ322-22-22-2-22002-22-22-2-222-2-220000-22-220000000000000000000000−2i2i2i−2i0000
χ332-22-22-2-22002-22-2-222-22-2-222i−2i−2i2i2-22-2000000002i−2i−2i2i000000000000000000
χ342-22-22-2-22002-22-2-222-22-2-22−2i2i2i−2i2-22-200000000−2i2i2i−2i000000000000000000
χ352-22-2-111-1002-22-2-222-2-111-12i−2i−2i2i-11-1100000000−iii−i−i3i3i3−i3−333−30000000000
χ362-22-2-111-1002-22-2-222-2-111-12i−2i−2i2i-11-1100000000−iii−ii3−i3−i3i33−3−330000000000
χ372-22-2-111-1002-22-2-222-2-111-1−2i2i2i−2i-11-1100000000i−i−ii−i3i3i3−i33−3−330000000000
χ382-22-2-111-1002-22-2-222-2-111-1−2i2i2i−2i-11-1100000000i−i−iii3−i3−i3i3−333−30000000000
χ392-2-2222-2-22-22-2-22-2-22222-2-20000-2-22222-2-20000000000000000-2200000000
χ402-2-2222-2-2-222-2-22-2-22222-2-20000-2-222-2-22200000000000000002-200000000
χ412-2-22-1-111002-2-2222-2-2-1-11122-2-2-1-11100002i−2i2i−2i-1-111−i−iii−i−iii0000000000
χ422-2-22-1-111002-2-2222-2-2-1-11122-2-2-1-1110000−2i2i−2i2i-1-111ii−i−iii−i−i0000000000
χ432-2-22-1-111002-2-2222-2-2-1-111-2-222-1-11100002i−2i−2i2i11-1-1−i−iiiii−i−i0000000000
χ442-2-22-1-111002-2-2222-2-2-1-111-2-222-1-1110000−2i2i2i−2i11-1-1ii−i−i−i−iii0000000000
χ454444-2-2-2-2004444-4-4-4-4-2-2-2-200002222000000000000000000000000000000
χ4644-4-4-22-220044-4-44-44-4-22-2200002-2-22000000000000000000000000000000
χ474-44-4-222-2004-44-44-4-44-222-200002-22-2000000000000000000000000000000
χ484-4-44-2-222004-4-44-4-444-2-222000022-2-2000000000000000000000000000000
χ498888888888-1-1-1-10000-1-1-1-100000000-1-1-1-100000000000000000000000000
χ5088888888-8-8-1-1-1-10000-1-1-1-100000000111100000000000000000000000000
χ5188-8-88-88-800-1-1110000-11-11000000003i−3i3i−3i00000000000000000000000000
χ5288-8-88-88-800-1-1110000-11-1100000000−3i3i−3i3i00000000000000000000000000
χ538-88-88-8-8800-11-110000-111-1000000003i−3i−3i3i00000000000000000000000000
χ548-88-88-8-8800-11-110000-111-100000000−3i3i3i−3i00000000000000000000000000
χ558-8-8888-8-88-8-111-10000-1-11100000000-1-11100000000000000000000000000
χ568-8-8888-8-8-88-111-10000-1-1110000000011-1-100000000000000000000000000
χ5716161616-8-8-8-800-2-2-2-20000111100000000000000000000000000000000000000
χ581616-16-16-88-8800-2-22200001-11-100000000000000000000000000000000000000
χ5916-1616-16-888-800-22-2200001-1-1100000000000000000000000000000000000000
χ6016-16-1616-8-88800-222-2000011-1-100000000000000000000000000000000000000

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