Finite Group Databasebeta

← Group #13049448

Character table — Group #13049448

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size112222444444444488888888888888181818363636363636363636363636545454545454108108108
order12336633333666663333333666666641212412121212121212121212128824242424266
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-11-1-111-1-1-1-1-1-1111111-1-1-1
χ4111111111111111111111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1111
χ5222222222222222222222222222222-2-2-20-200-2-2000000000000000
χ6222-12-12-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-122-1-1-1-1000000000
χ7222-12-12-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-1222-2-111-1-1-2-21111000000000
χ8222-12-12-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-1-2-2-201−i3i31100−i3−i3i3i3000000000
χ9222-12-12-1-1-1222-1-1-122-1-1-1-1-122-1-1-1-1-1-2-2-201i3−i31100i3i3−i3−i3000000000
χ1022-12-12222-122222-1-1-12-1-1-1-1-1-12-1-1-1-12-1-10200-1-100000022-1-1-1-1000
χ1122-12-12222-122222-1-1-12-1-1-1-1-1-12-1-1-1-12-1-10200-1-1000000-2-21111000
χ1222-12-12222-122222-1-1-12-1-1-1-1-1-12-1-1-1-1-2110-200110000000033−3−3000
χ1322-12-12222-122222-1-1-12-1-1-1-1-1-12-1-1-1-1-2110-2001100000000−3−333000
χ142-222-2-222222-2-2-2-2-22222222-2-2-2-2-2-2-2000000000000000−i2i2−i2i2−i2i2000
χ152-222-2-222222-2-2-2-2-22222222-2-2-2-2-2-2-2000000000000000i2−i2i2−i2i2−i2000
χ162-2-121-2222-12-2-2-2-21-1-12-1-1-1-111-2111103−300003−3000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ172-2-121-2222-12-2-2-2-21-1-12-1-1-1-111-2111103−300003−3000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ182-2-121-2222-12-2-2-2-21-1-12-1-1-1-111-211110−330000−33000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ192-2-121-2222-12-2-2-2-21-1-12-1-1-1-111-211110−330000−33000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ204444441114-2-211141-2-211-2-21-2-211-2-2000202200-1-1-1-1-1-1000000000
χ214444441114-2-211141-2-211-2-21-2-211-2-2000-20-2-200111111000000000
χ22444444-2-2-2411-2-2-24-211-2-211-211-2-2110000000000000000000002-1-1
χ23444444-2-2-2411-2-2-24-211-2-211-211-2-211000000000000000000000-211
χ24444-24-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-21-21−1−3i32−1+3i32111-21−1−3i32−1+3i321100020−1−i3−1+i300-1-11+i321+i321−i321−i32000000000
χ25444-24-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-21-21−1−3i32−1+3i32111-21−1−3i32−1+3i3211000-201+i31−i30011−1−i32−1−i32−1+i32−1+i32000000000
χ26444-24-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-21-21−1+3i32−1−3i32111-21−1+3i32−1−3i321100020−1+i3−1−i300-1-11−i321−i321+i321+i32000000000
χ27444-24-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-21-21−1+3i32−1−3i32111-21−1+3i32−1−3i3211000-201−i31+i30011−1+i32−1+i32−1−i32−1−i32000000000
χ2844-2-2-2-24-2-21444-2-21-2-2-21111-2-2-211114-2-20-20011000000000000000
χ2944-2-2-2-24-2-21444-2-21-2-2-21111-2-2-21111-4220200-1-1000000000000000
χ304-444-4-41114-22-1-1-1-41-2-211-2-2-122-1-1220000000003−33−33−3000000000
χ314-444-4-41114-22-1-1-1-41-2-211-2-2-122-1-122000000000−33−33−33000000000
χ324-444-4-4-2-2-241-1222-4-211-2-2112-1-122-1-10000000000000000000000−i3i3
χ334-444-4-4-2-2-241-1222-4-211-2-2112-1-122-1-10000000000000000000000i3−i3
χ344-44-2-421−1−3i32−1+3i32-2-22-11+3i321−3i3221-21−1−3i32−1+3i3211-12-11+3i321−3i32-1-10000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000
χ354-44-2-421−1−3i32−1+3i32-2-22-11+3i321−3i3221-21−1−3i32−1+3i3211-12-11+3i321−3i32-1-1000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000
χ364-44-2-421−1+3i32−1−3i32-2-22-11−3i321+3i3221-21−1+3i32−1−3i3211-12-11−3i321+3i32-1-10000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000
χ374-44-2-421−1+3i32−1−3i32-2-22-11−3i321+3i3221-21−1+3i32−1−3i3211-12-11−3i321+3i32-1-1000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000
χ384-44-2-424-2-2-24-4-422244-2-2-2-2-2-4-422222000000000000000000000000
χ394-4-2-2224-2-214-4-422-1-2-2-21111222-1-1-1-1023−230000−33000000000000000
χ404-4-2-2224-2-214-4-422-1-2-2-21111222-1-1-1-10−232300003−3000000000000000
χ41888-48-4-422-422-422-4-42-122-1-1-42-122-1-1000000000000000000000000
χ4288-48-48222-4-4-4222-4-12-4-1-122-12-4-1-122000000000000000000000000
χ4388-48-48-4-4-4-422-4-4-4-42-1222-1-12-1222-1-1000000000000000000000000
χ4488-4-4-4-42−1−3i3−1+3i32-4-42−1−3i3−1+3i32-1221+3i321−3i32-1-1-1221+3i321−3i32-1-1000000000000000000000000
χ4588-4-4-4-42−1+3i3−1−3i32-4-42−1+3i3−1−3i32-1221−3i321+3i32-1-1-1221−3i321+3i32-1-1000000000000000000000000
χ4688-4-4-4-4-422222-42222-1-1-1-15-42-1-1-1-15-4000000000000000000000000
χ4788-4-4-4-4-422222-42222-1-1-1-1-452-1-1-1-1-45000000000000000000000000
χ488-88-4-84-422-42-24-2-24-42-122-1-14-21-2-211000000000000000000000000
χ498-8-484-8222-4-44-2-2-24-12-4-1-1221-2411-2-2000000000000000000000000
χ508-8-484-8-4-4-4-42-244442-1222-1-1-21-2-2-211000000000000000000000000
χ518-8-4-4442−1−3i3−1+3i32-44-21+3i31−3i3-2-1221+3i321−3i32-1-11-2-2−1−3i32−1+3i3211000000000000000000000000
χ528-8-4-4442−1+3i3−1−3i32-44-21−3i31+3i3-2-1221−3i321+3i32-1-11-2-2−1+3i32−1−3i3211000000000000000000000000
χ538-8-4-444-42222-24-2-2-22-1-1-1-15-4-21111-54000000000000000000000000
χ548-8-4-444-42222-24-2-2-22-1-1-1-1-45-211114-5000000000000000000000000

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