Finite Group Databasebeta

← Group #13180867

Character table — Group #13180867

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222222244444668812121212161616161616161616161616161616161618181818242436363636363636363636365454727272727272144144
order12334661212361212122436661212333366661212121212121212122288612244488824242424446121212242466
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ3111111111111111111111111111111111111111-1-1111111-1-11-1-11111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-111-111-1-1-1-1-1-1-1-11111-1-1
χ51111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-11-111-11-111-1-11-111-1-11-1-111-11-11-1
χ61111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-11-1-1111-11-1-11-111-1
χ71111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1111-11-11-11-1-1111-1-1-11-11-11-11-11
χ81111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-11-111-1-1-111-111-11-11-1-11
χ92222222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200220000000000022000000-1-1
χ102222222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200000000000-2-200000011
χ112222-222-2-222-2-2-2-22-1-1-2-222-1-1-1-1-1-1-1-11111111112-200-22000000000002-2000000-11
χ122222-222-2-222-2-2-2-22-1-1-2-222-1-1-1-1-1-1-1-1111111111-2200-2200000000000-220000001-1
χ13222-12-12-1-1-1-12-1-122222-1-122-1-1-12-1-1-1222-1-1-1-1-1-10022-1-12200200-1-1-1-100-1-1000000
χ14222-12-12-1-1-1-12-1-122222-1-122-1-1-12-1-1-1222-1-1-1-1-1-100-2-2-1-1-2-200-20011110011000000
χ15222-1-2-1211-1-1-211-2222-21-122-1-1-12-1-1-1-2-2-211111100221-1-2200-200-1-111001-1000000
χ16222-1-2-1211-1-1-211-2222-21-122-1-1-12-1-1-1-2-2-211111100-2-21-12-20020011-1-100-11000000
χ1722-1222-122-1-1-1-1-12222-122-1-12-1-1-12-1-12-1-122-1-1-1-10000-1-1002202200000000-1-1-1-100
χ1822-1222-122-1-1-1-1-12222-122-1-12-1-1-12-1-12-1-122-1-1-1-10000-1-100-2-20-2-200000000111100
χ1922-12-22-1-2-2-1-1111-22221-22-1-12-1-1-12-1-1-211-2-2111100001-1002-202-200000000-11-1100
χ2022-12-22-1-2-2-1-1111-22221-22-1-12-1-1-12-1-1-211-2-2111100001-100-220-22000000001-11-100
χ2133333333333333-1-100-1-1-1-1000000000000000003311-1-1-1-1-1-11111111-1-1-1-1-1-11100
χ2233333333333333-1-100-1-1-1-10000000000000000033-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-100
χ2333333333333333-1-100-1-1-1-100000000000000000-3-311-1-1-1-1111-1-1111111-1-111-1-100
χ2433333333333333-1-100-1-1-1-100000000000000000-3-3-1-1-1-111-1-1-111-1-1-1-11111-1-11100
χ253333-333-3-333-3-3-31-10011-1-1000000000000000003-3111-11-1-11-11-111-1-1-111-1-111-100
χ263333-333-3-333-3-3-31-10011-1-1000000000000000003-3-1-11-1-111-11-11-1-111-11-111-1-1100
χ273333-333-3-333-3-3-31-10011-1-100000000000000000-33111-11-11-1-1-1111-1-11-11-11-1-1100
χ283333-333-3-333-3-3-31-10011-1-100000000000000000-33-1-11-1-11-1111-1-1-1111-1-11-111-100
χ29444-24-24-2-2-2-24-2-244-2-24-2-24-2111-2111-2-2-21111110000-2-2000000000000000000000
χ30444-2-4-2422-2-2-422-44-2-2-42-24-2111-2111222-1-1-1-1-1-100002-2000000000000000000000
χ3144-2444-244-2-2-2-2-244-2-2-244-21-2111-211-211-2-211110000-2-2000000000000000000000
χ3244-24-44-2-4-4-2-2222-44-2-22-44-21-2111-2112-1-122-1-1-1-100002-2000000000000000000000
χ3344-2-24-2-2-2-211-2114444-2-2-2-2-2-211-2-2114-2-2-2-21111000011000000000000000000000
χ3444-2-24-2-2-2-211-21144-2-2-2-2-2-211−1−3i32−1+3i3211−1−3i32−1+3i32-21111−1−3i32−1−3i32−1+3i32−1+3i32000011000000000000000000000
χ3544-2-24-2-2-2-211-21144-2-2-2-2-2-211−1+3i32−1−3i3211−1+3i32−1−3i32-21111−1+3i32−1+3i32−1−3i32−1−3i32000011000000000000000000000
χ3644-2-2-4-2-222112-1-1-444422-2-2-2-211-2-211-42222-1-1-1-10000-11000000000000000000000
χ3744-2-2-4-2-222112-1-1-44-2-222-2-211−1−3i32−1+3i3211−1−3i32−1+3i322-1-1-1-11+3i321+3i321−3i321−3i320000-11000000000000000000000
χ3844-2-2-4-2-222112-1-1-44-2-222-2-211−1+3i32−1−3i3211−1+3i32−1−3i322-1-1-1-11−3i321−3i321+3i321+3i320000-11000000000000000000000
χ394-4440-4-4004-400000-220000-2-2-2-222220000000000022−2200000000022−22000000000000
χ404-4440-4-4004-400000-220000-2-2-2-2222200000000000−2222000000000−2222000000000000
χ414-44-202-423−23-22023−2300-220000-21112-1-1-10003−33−33−30022−22000000000−226−60000000000
χ424-44-202-423−23-22023−2300-220000-21112-1-1-10003−33−33−300−22220000000002−2−660000000000
χ434-44-202-4−2323-220−232300-220000-21112-1-1-1000−33−33−330022−22000000000−22−660000000000
χ444-44-202-4−2323-220−232300-220000-21112-1-1-1000−33−33−3300−22220000000002−26−60000000000
χ45666-36-36-3-3-3-36-3-3-2-200-211-200000000000000000002211-2-200200-1-1-1-10011000000
χ46666-36-36-3-3-3-36-3-3-2-200-211-20000000000000000000-2-2112200-200111100-1-1000000
χ47666-3-6-3633-3-3-6332-2002-11-2000000000000000000022-112-200-200-1-11100-11000000
χ48666-3-6-3633-3-3-6332-2002-11-20000000000000000000-2-2-11-220020011-1-1001-1000000
χ4966-3666-366-3-3-3-3-3-2-2001-2-210000000000000000000001100220-2-200000000-1-11100
χ5066-3666-366-3-3-3-3-3-2-2001-2-210000000000000000000001100-2-20220000000011-1-100
χ5166-36-66-3-6-6-3-33332-200-12-21000000000000000000000-11002-20-2200000000-111-100
χ5266-36-66-3-6-6-3-33332-200-12-21000000000000000000000-1100-2202-2000000001-1-1100
χ538-8880-8-8008-8000002-200002222-2-2-2-2000000000000000000000000000000000000
χ548-88-404-843−43-44043−43002-200002-1-1-1-2111000−33−33−33000000000000000000000000000
χ558-88-404-8−4343-440−4343002-200002-1-1-1-21110003−33−33−3000000000000000000000000000
χ568-8-480-8400-44000002-20000-12-1-11-21103i−3i003i−3i−3i3i000000000000000000000000000
χ578-8-480-8400-44000002-20000-12-1-11-2110−3i3i00−3i3i3i−3i000000000000000000000000000
χ588-8-480-8400-4400000-4400002-422-24-2-2000000000000000000000000000000000000
χ598-8-4-404443−432-20−2323002-20000-1-11−3i321+3i3211−1+3i32−1−3i320−3i3i−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000000000000
χ608-8-4-404443−432-20−2323002-20000-1-11+3i321−3i3211−1−3i32−1+3i3203i−3i−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000000000000
χ618-8-4-404443−432-20−232300-44000022-1-1-2-21100023−23−33−33000000000000000000000000000
χ628-8-4-4044−43432-2023−23002-20000-1-11−3i321+3i3211−1+3i32−1−3i3203i−3i3−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000000000000
χ638-8-4-4044−43432-2023−23002-20000-1-11+3i321−3i3211−1−3i32−1+3i320−3i3i3−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000000000000
χ648-8-4-4044−43432-2023−2300-44000022-1-1-2-211000−23233−33−3000000000000000000000000000
χ651212-6-612-6-6-6-633-633-4-4002222000000000000000000000-1-1000000000000000000000
χ661212-6-6-12-6-666336-3-34-400-2-2220000000000000000000001-1000000000000000000000

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