Finite Group Databasebeta

← Group #13165760

Character table — Group #13165760

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222266888899991616161618181818181818182424242436363636363636363636363636363636545454545454108108108108
order124436121288361212224436121244446612122424242488881212121224242424242424248888884444
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
χ911-1-111-1-1i−i11-1-111-1-111-1-111-1-111-1-1ii−i−ii−ii−i11-1-1ii−i−iii−i−ii−iii−i−i1-11-1
χ1011-1-111-1-1i−i11-1-111-1-111-1-111-1-111-1-1ii−i−i−ii−ii11-1-1−i−iii−i−iiii−iii−i−i-11-11
χ1111-1-111-1-1i−i11-1-111-1-111-1-1-1-11111-1-1ii−i−ii−i−ii-1-111ii−i−i−i−iiii−i−i−iii1-1-11
χ1211-1-111-1-1i−i11-1-111-1-111-1-1-1-11111-1-1ii−i−i−iii−i-1-111−i−iiiii−i−ii−i−i−iii-111-1
χ1311-1-111-1-1−ii11-1-111-1-111-1-111-1-111-1-1−i−iiii−ii−i11-1-1ii−i−iii−i−i−ii−i−iii-11-11
χ1411-1-111-1-1−ii11-1-111-1-111-1-111-1-111-1-1−i−iii−ii−ii11-1-1−i−iii−i−iii−ii−i−iii1-11-1
χ1511-1-111-1-1−ii11-1-111-1-111-1-1-1-11111-1-1−i−iiii−i−ii-1-111ii−i−i−i−iii−iiii−i−i-111-1
χ1611-1-111-1-1−ii11-1-111-1-111-1-1-1-11111-1-1−i−iii−iii−i-1-111−i−iiiii−i−i−iiii−i−i1-1-11
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
χ2322-2-222-2-22i−2i22-2-2-2-22222-2-20000-2-2222i2i−2i−2i0000000000000000−2i2i00000000
χ2422-2-222-2-2−2i2i22-2-2-2-22222-2-20000-2-222−2i−2i2i2i00000000000000002i−2i00000000
χ2522-2-2-1-1110022-2-222-2-2-1-11122-2-2-1-11100002i−2i2i−2i-1-111−i−iii−i−iii0000000000
χ2622-2-2-1-1110022-2-222-2-2-1-11122-2-2-1-1110000−2i2i−2i2i-1-111ii−i−iii−i−i0000000000
χ2722-2-2-1-1110022-2-222-2-2-1-111-2-222-1-11100002i−2i−2i2i11-1-1−i−iiiii−i−i0000000000
χ2822-2-2-1-1110022-2-222-2-2-1-111-2-222-1-1110000−2i2i2i−2i11-1-1ii−i−i−i−iii0000000000
χ292-22i−2i2-22i−2i002-22i−2i2-22i−2i2-22i−2i00002-22i−2i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ302-22i−2i2-22i−2i002-22i−2i2-22i−2i2-22i−2i00002-22i−2i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ312-22i−2i2-22i−2i002-22i−2i-22−2i2i2-22i−2i2i−2i2-2-22−2i2i000000002i−2i2-2000000000000000000
χ322-22i−2i2-22i−2i002-22i−2i-22−2i2i2-22i−2i−2i2i-22-22−2i2i00000000−2i2i-22000000000000000000
χ332-22i−2i-11−ii002-22i−2i-22−2i2i-11−ii2i−2i2-21-1i−i00000000−ii-11ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ342-22i−2i-11−ii002-22i−2i-22−2i2i-11−ii2i−2i2-21-1i−i00000000−ii-11−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ352-22i−2i-11−ii002-22i−2i-22−2i2i-11−ii−2i2i-221-1i−i00000000i−i1-1ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ362-22i−2i-11−ii002-22i−2i-22−2i2i-11−ii−2i2i-221-1i−i00000000i−i1-1−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ372-2−2i2i2-2−2i2i002-2−2i2i2-2−2i2i2-2−2i2i00002-2−2i2i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ382-2−2i2i2-2−2i2i002-2−2i2i2-2−2i2i2-2−2i2i00002-2−2i2i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ392-2−2i2i2-2−2i2i002-2−2i2i-222i−2i2-2−2i2i2i−2i-22-222i−2i000000002i−2i-22000000000000000000
χ402-2−2i2i2-2−2i2i002-2−2i2i-222i−2i2-2−2i2i−2i2i2-2-222i−2i00000000−2i2i2-2000000000000000000
χ412-2−2i2i-11i−i002-2−2i2i-222i−2i-11i−i2i−2i-221-1−ii00000000−ii1-1−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ422-2−2i2i-11i−i002-2−2i2i-222i−2i-11i−i2i−2i-221-1−ii00000000−ii1-1ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ432-2−2i2i-11i−i002-2−2i2i-222i−2i-11i−i−2i2i2-21-1−ii00000000i−i-11−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ442-2−2i2i-11i−i002-2−2i2i-222i−2i-11i−i−2i2i2-21-1−ii00000000i−i-11ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ454444-2-2-2-2004444-4-4-4-4-2-2-2-200002222000000000000000000000000000000
χ4644-4-4-2-2220044-4-4-4-444-2-222000022-2-2000000000000000000000000000000
χ474-44i−4i-22−2i2i004-44i−4i4-44i−4i-22−2i2i0000-22−2i2i000000000000000000000000000000
χ484-4−4i4i-222i−2i004-4−4i4i4-4−4i4i-222i−2i0000-222i−2i000000000000000000000000000000
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
χ538-88i−8i8-88i−8i00-11−ii0000-11−ii000000003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ1300000000000000000000000000
χ548-88i−8i8-88i−8i00-11−ii0000-11−ii00000000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ1300000000000000000000000000
χ558-8−8i8i8-8−8i8i00-11i−i0000-11i−i00000000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ2300000000000000000000000000
χ568-8−8i8i8-8−8i8i00-11i−i0000-11i−i000000003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ2300000000000000000000000000
χ5716161616-8-8-8-800-2-2-2-20000111100000000000000000000000000000000000000
χ581616-16-16-8-88800-2-222000011-1-100000000000000000000000000000000000000
χ5916-1616i−16i-88−8i8i00-22−2i2i00001-1i−i00000000000000000000000000000000000000
χ6016-16−16i16i-888i−8i00-222i−2i00001-1−ii00000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.