Finite Group Databasebeta

← Group #13167648

Character table — Group #13167648

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244888888888888888888888888999918181818181836363636363636363636363636365454545454545454108108108108
order1244368812122424333666121212121212242424242424242424242424224466881212448812121212242424242424444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-111i−i-1-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111i−i-1-11-1i−i11-1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ1011-1-111i−i-1-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111i−i-1-11-1i−i11-1-1i−iii−i−i-1-111−i−iii-11−ii
χ1111-1-111i−i-1-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111i−i-1-1-11−ii-1-111i−i−i−iii11-1-1ii−i−i-11−ii
χ1211-1-111i−i-1-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-111i−i-1-1-11−ii-1-111i−i−i−iii-1-111−i−iii1-1i−i
χ1311-1-111−ii-1-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111−ii-1-11-1−ii11-1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ1411-1-111−ii-1-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111−ii-1-11-1−ii11-1-1−ii−i−iii-1-111ii−i−i-11i−i
χ1511-1-111−ii-1-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111−ii-1-1-11i−i-1-111−iiii−i−i11-1-1−i−iii-11i−i
χ1611-1-111−ii-1-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii11-1-111−ii-1-1-11i−i-1-111−iiii−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000-2-20000000000000000
χ18222222-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-200000000220000000000000000
χ192222-1-122-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1000000000000
χ202222-1-122-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-122-1-1-2-2-2-21111-1-11111000000000000
χ212222-1-122-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211-2-21100003−33−3113−33−3000000000000
χ222222-1-122-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-211-2-2110000−33−3311−33−33000000000000
χ232222-1-1-2-2-1-1112-1-12-1-122-1-1-1-1-2-21111-2-211112222-1-1-2-2-1-122-2-2-1-1-1-1111111000000000000
χ242222-1-1-2-2-1-1112-1-12-1-122-1-1-1-1-2-21111-2-211112222-1-1-2-2-1-1-2-222111111-1-1-1-1000000000000
χ252222-1-1-2-2-1-1112-1-12-1-122-1-1-1-1-2-21111-2-21111-2-2-2-211221100003−33−3-1-1−33−33000000000000
χ262222-1-1-2-2-1-1112-1-12-1-122-1-1-1-1-2-21111-2-21111-2-2-2-21122110000−33−33-1-13−33−3000000000000
χ2722-2-2222i−2i-2-22i−2i222222-2-2-2-2-2-22i2i2i2i2i2i−2i−2i−2i−2i−2i−2i-2-222-2-2−2i2i2200000000−2i2i0000000000000000
χ2822-2-222−2i2i-2-2−2i2i222222-2-2-2-2-2-2−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i-2-222-2-22i−2i22000000002i−2i0000000000000000
χ2922-2-2-1-12i−2i11−ii2-1-12-1-1-2-211112i2i−i−i−i−i−2i−2iiiii22-2-2-1-12i−2i112-22i−2i-1-111−ii−i−iii000000000000
χ3022-2-2-1-12i−2i11−ii2-1-12-1-1-2-211112i2i−i−i−i−i−2i−2iiiii22-2-2-1-12i−2i11-22−2i2i11-1-1−iiii−i−i000000000000
χ3122-2-2-1-12i−2i11−ii2-1-12-1-1-2-211112i2i−i−i−i−i−2i−2iiiii-2-22211−2i2i-1-100003−3−33i−ii3−i3−i3i3000000000000
χ3222-2-2-1-12i−2i11−ii2-1-12-1-1-2-211112i2i−i−i−i−i−2i−2iiiii-2-22211−2i2i-1-10000−333−3i−i−i3i3i3−i3000000000000
χ3322-2-2-1-1−2i2i11i−i2-1-12-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i22-2-2-1-1−2i2i112-2−2i2i-1-111i−iii−i−i000000000000
χ3422-2-2-1-1−2i2i11i−i2-1-12-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i22-2-2-1-1−2i2i11-222i−2i11-1-1i−i−i−iii000000000000
χ3522-2-2-1-1−2i2i11i−i2-1-12-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i-2-222112i−2i-1-100003−3−33−ii−i3i3i3−i3000000000000
χ3622-2-2-1-1−2i2i11i−i2-1-12-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i-2-222112i−2i-1-10000−333−3−iii3−i3−i3i3000000000000
χ372-22i−2i2-2002i−2i00222-2-2-22i−2i2i2i−2i−2i0000000000002-22i−2i2-2002i−2i0000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ382-22i−2i2-2002i−2i00222-2-2-22i−2i2i2i−2i−2i0000000000002-22i−2i2-2002i−2i000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ392-22i−2i2-2002i−2i00222-2-2-22i−2i2i2i−2i−2i000000000000-22−2i2i-2200−2i2i000000000000002i−2i2-200000000
χ402-22i−2i2-2002i−2i00222-2-2-22i−2i2i2i−2i−2i000000000000-22−2i2i-2200−2i2i00000000000000−2i2i-2200000000
χ412-2−2i2i2-200−2i2i00222-2-2-2−2i2i−2i−2i2i2i0000000000002-2−2i2i2-200−2i2i000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ422-2−2i2i2-200−2i2i00222-2-2-2−2i2i−2i−2i2i2i0000000000002-2−2i2i2-200−2i2i0000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ432-2−2i2i2-200−2i2i00222-2-2-2−2i2i−2i−2i2i2i000000000000-222i−2i-22002i−2i000000000000002i−2i-2200000000
χ442-2−2i2i2-200−2i2i00222-2-2-2−2i2i−2i−2i2i2i000000000000-222i−2i-22002i−2i00000000000000−2i2i2-200000000
χ454-44i−4i-2200−2i2i004-2-2-4224i−4i−2i−2i2i2i0000000000004-44i−4i-2200−2i2i00000000000000000000000000
χ464-44i−4i-2200−2i2i004-2-2-4224i−4i−2i−2i2i2i000000000000-44−4i4i2-2002i−2i00000000000000000000000000
χ474-4−4i4i-22002i−2i004-2-2-422−4i4i2i2i−2i−2i0000000000004-4−4i4i-22002i−2i00000000000000000000000000
χ484-4−4i4i-22002i−2i004-2-2-422−4i4i2i2i−2i−2i000000000000-444i−4i2-200−2i2i00000000000000000000000000
χ49888888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ50888888-8-888-8-8-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000000000000000
χ518888-4-488-4-4-4-4-11−3i321+3i32-11−3i321+3i32-1-11−3i321+3i321−3i321+3i32-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000000000
χ528888-4-488-4-4-4-4-11+3i321−3i32-11+3i321−3i32-1-11+3i321−3i321+3i321−3i32-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000000000
χ538888-4-4-8-8-4-444-11−3i321+3i32-11−3i321+3i32-1-11−3i321+3i321−3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000000000000000000
χ548888-4-4-8-8-4-444-11+3i321−3i32-11+3i321−3i32-1-11+3i321−3i321+3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000000000000000000
χ5588-8-8888i−8i-8-88i−8i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii000000000000000000000000000000000000
χ5688-8-888−8i8i-8-8−8i8i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i000000000000000000000000000000000000
χ5788-8-8-4-48i−8i44−4i4i-11−3i321+3i32-11−3i321+3i3211−1+3i32−1−3i32−1+3i32−1−3i32−i−i−2ζ14+ζ22−2ζ14+ζ22ζ14−2ζ22ζ14−2ζ22ii2ζ14−ζ222ζ14−ζ22−ζ14+2ζ22−ζ14+2ζ22000000000000000000000000000000000000
χ5888-8-8-4-48i−8i44−4i4i-11+3i321−3i32-11+3i321−3i3211−1−3i32−1+3i32−1−3i32−1+3i32−i−iζ14−2ζ22ζ14−2ζ22−2ζ14+ζ22−2ζ14+ζ22ii−ζ14+2ζ22−ζ14+2ζ222ζ14−ζ222ζ14−ζ22000000000000000000000000000000000000
χ5988-8-8-4-4−8i8i444i−4i-11−3i321+3i32-11−3i321+3i3211−1+3i32−1−3i32−1+3i32−1−3i32ii2ζ14−ζ222ζ14−ζ22−ζ14+2ζ22−ζ14+2ζ22−i−i−2ζ14+ζ22−2ζ14+ζ22ζ14−2ζ22ζ14−2ζ22000000000000000000000000000000000000
χ6088-8-8-4-4−8i8i444i−4i-11+3i321−3i32-11+3i321−3i3211−1−3i32−1+3i32−1−3i32−1+3i32ii−ζ14+2ζ22−ζ14+2ζ222ζ14−ζ222ζ14−ζ22−i−iζ14−2ζ22ζ14−2ζ22−2ζ14+ζ22−2ζ14+ζ22000000000000000000000000000000000000
χ618-88i−8i8-8008i−8i00-1-1-1111−ii−i−iii3ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13000000000000000000000000000000000000
χ628-88i−8i8-8008i−8i00-1-1-1111−ii−i−iii−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ13000000000000000000000000000000000000
χ638-88i−8i-4400−4i4i00-11−3i321+3i321−1+3i32−1−3i32−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ223ζ7+3ζ23−3ζ7−3ζ23−3ζ73ζ7−3ζ233ζ23−3ζ5−3ζ133ζ5+3ζ133ζ13−3ζ133ζ5−3ζ5000000000000000000000000000000000000
χ648-88i−8i-4400−4i4i00-11−3i321+3i321−1+3i32−1−3i32−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ22−3ζ7−3ζ233ζ7+3ζ233ζ7−3ζ73ζ23−3ζ233ζ5+3ζ13−3ζ5−3ζ13−3ζ133ζ13−3ζ53ζ5000000000000000000000000000000000000
χ658-88i−8i-4400−4i4i00-11+3i321−3i321−1−3i32−1+3i32−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ223ζ7+3ζ23−3ζ7−3ζ23−3ζ233ζ23−3ζ73ζ7−3ζ5−3ζ133ζ5+3ζ133ζ5−3ζ53ζ13−3ζ13000000000000000000000000000000000000
χ668-88i−8i-4400−4i4i00-11+3i321−3i321−1−3i32−1+3i32−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ22−3ζ7−3ζ233ζ7+3ζ233ζ23−3ζ233ζ7−3ζ73ζ5+3ζ13−3ζ5−3ζ13−3ζ53ζ5−3ζ133ζ13000000000000000000000000000000000000
χ678-8−8i8i8-800−8i8i00-1-1-1111i−iii−i−i−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ23000000000000000000000000000000000000
χ688-8−8i8i8-800−8i8i00-1-1-1111i−iii−i−i3ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23000000000000000000000000000000000000
χ698-8−8i8i-44004i−4i00-11−3i321+3i321−1+3i32−1−3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−3ζ5−3ζ133ζ5+3ζ133ζ13−3ζ133ζ5−3ζ53ζ7+3ζ23−3ζ7−3ζ23−3ζ73ζ7−3ζ233ζ23000000000000000000000000000000000000
χ708-8−8i8i-44004i−4i00-11−3i321+3i321−1+3i32−1−3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ223ζ5+3ζ13−3ζ5−3ζ13−3ζ133ζ13−3ζ53ζ5−3ζ7−3ζ233ζ7+3ζ233ζ7−3ζ73ζ23−3ζ23000000000000000000000000000000000000
χ718-8−8i8i-44004i−4i00-11+3i321−3i321−1−3i32−1+3i32i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−3ζ5−3ζ133ζ5+3ζ133ζ5−3ζ53ζ13−3ζ133ζ7+3ζ23−3ζ7−3ζ23−3ζ233ζ23−3ζ73ζ7000000000000000000000000000000000000
χ728-8−8i8i-44004i−4i00-11+3i321−3i321−1−3i32−1+3i32i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ223ζ5+3ζ13−3ζ5−3ζ13−3ζ53ζ5−3ζ133ζ13−3ζ7−3ζ233ζ7+3ζ233ζ23−3ζ233ζ7−3ζ7000000000000000000000000000000000000

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