Finite Group Databasebeta

← Group #13180869

Character table — Group #13180869

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222222244444668812121212161616161616161616161616161616161618181818242436363636363636363636365454727272727272144144
order123346612123612121224366612123333666612121212121212121222886122224888242424244466612242466
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ3111111111111111111111111111111111111111-1-111111-1-111-1-11111-1-11-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-111-1-111-1-1-1-1-1-1-111-111-1-1
χ51111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-11-111-1111-1-1-11-111-1-11-111-1-11-11-1
χ61111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1111-11-1-1111-1-1-111-111-1
χ71111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1111-111-11-1-1-1111-1-1-111-11-1-11-11
χ81111-111-1-111-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-11-11-1111-1-1-111-11-11-111-1-11
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
χ13222-12-1222-1-1-1-1-122222-1-122-1-1-12-1-1-1222-1-1-1-1-1-10000-1-102200220000000-1-10-1-100
χ14222-12-1222-1-1-1-1-122222-1-122-1-1-12-1-1-1222-1-1-1-1-1-10000-1-10-2-200-2-200000001101100
χ15222-1-2-12-2-2-1-1111-2222-21-122-1-1-12-1-1-1-2-2-211111100001-102-2002-20000000-110-1100
χ16222-1-2-12-2-2-1-1111-2222-21-122-1-1-12-1-1-1-2-2-211111100001-10-2200-2200000001-101-100
χ1722-1222-1-1-1-1-12-1-12222-122-1-12-1-1-12-1-12-1-122-1-1-1-10022-1-12002200-1-1-1-100-100-10000
χ1822-1222-1-1-1-1-12-1-12222-122-1-12-1-1-12-1-12-1-122-1-1-1-100-2-2-1-1-200-2-20011110010010000
χ1922-12-22-111-1-1-211-22221-22-1-12-1-1-12-1-1-211-2-2111100221-1200-2-200-1-11100-10010000
χ2022-12-22-111-1-1-211-22221-22-1-12-1-1-12-1-1-211-2-2111100-2-21-1-200220011-1-100100-10000
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
χ2333333333333333-1-100-1-1-1-100000000000000000-3-311-1-1-111-11-1-1111111-111-1-1-100
χ2433333333333333-1-100-1-1-1-100000000000000000-3-3-1-1-1-11-1-11-111-1-1-1-1111-1-111100
χ253333-333-3-333-3-3-31-10011-1-1000000000000000003-3111-1-1-111-11-111-1-1-11-1-1111-100
χ263333-333-3-333-3-3-31-10011-1-1000000000000000003-3-1-11-111-1-11-11-1-111-1111-1-1-1100
χ273333-333-3-333-3-3-31-10011-1-100000000000000000-33111-1-11-11-1-1111-1-11-1-11-11-1100
χ283333-333-3-333-3-3-31-10011-1-100000000000000000-33-1-11-11-11-111-1-1-1111-11-11-11-100
χ29444-24-2444-2-2-2-2-244-2-24-2-24-2111-2111-2-2-21111110000-2-2000000000000000000000
χ30444-2-4-24-4-4-2-2222-44-2-2-42-24-2111-2111222-1-1-1-1-1-100002-2000000000000000000000
χ3144-2444-2-2-2-2-24-2-244-2-2-244-21-2111-211-211-2-211110000-2-2000000000000000000000
χ3244-24-44-222-2-2-422-44-2-22-44-21-2111-2112-1-122-1-1-1-100002-2000000000000000000000
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
χ394-4440-4-4004-400000-220000-2-2-2-2222200000000000−2i22i2000000000−2i22i2000000000000
χ404-4440-4-4004-400000-220000-2-2-2-22222000000000002i2−2i20000000002i2−2i2000000000000
χ414-4-240-4223−23-22023−2300-2200001-211-12-1-103−3003−33−300−2i22i2000000000i2−i2i6−i60000000000
χ424-4-240-4223−23-22023−2300-2200001-211-12-1-103−3003−33−3002i2−2i2000000000−i2i2−i6i60000000000
χ434-4-240-42−2323-220−232300-2200001-211-12-1-10−3300−33−3300−2i22i2000000000i2−i2−i6i60000000000
χ444-4-240-42−2323-220−232300-2200001-211-12-1-10−3300−33−33002i2−2i2000000000−i2i2i6−i60000000000
χ45666-36-3666-3-3-3-3-3-2-200-211-20000000000000000000001102200-2-20000000-1-101100
χ46666-36-3666-3-3-3-3-3-2-200-211-2000000000000000000000110-2-200220000000110-1-100
χ47666-3-6-36-6-6-3-33332-2002-11-2000000000000000000000-1102-200-220000000-1101-100
χ48666-3-6-36-6-6-3-33332-2002-11-2000000000000000000000-110-22002-200000001-10-1100
χ4966-3666-3-3-3-3-36-3-3-2-2001-2-2100000000000000000002211-200-2200-1-1-1-10010010000
χ5066-3666-3-3-3-3-36-3-3-2-2001-2-210000000000000000000-2-2112002-200111100-100-10000
χ5166-36-66-333-3-3-6332-200-12-21000000000000000000022-11-2002-200-1-11100100-10000
χ5266-36-66-333-3-3-6332-200-12-210000000000000000000-2-2-11200-220011-1-100-10010000
χ538-8880-8-8008-8000002-200002222-2-2-2-2000000000000000000000000000000000000
χ548-88-404-800-44000002-200002-1-1-1-21110003i−3i3i−3i−3i3i000000000000000000000000000
χ558-88-404-800-44000002-200002-1-1-1-2111000−3i3i−3i3i3i−3i000000000000000000000000000
χ568-88-404-800-4400000-440000-42224-2-2-2000000000000000000000000000000000000
χ578-8-480-8443−43-44043−43002-20000-12-1-11-2110−3300−33−33000000000000000000000000000
χ588-8-480-84−4343-440−4343002-20000-12-1-11-21103−3003−33−3000000000000000000000000000
χ598-8-4-404443−432-20−2323002-20000-1-11−3i321+3i3211−1+3i32−1−3i320−33−3i3i−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000000000000
χ608-8-4-404443−432-20−2323002-20000-1-11+3i321−3i3211−1−3i32−1+3i320−333i−3iζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000000000000
χ618-8-4-404443−432-20−232300-44000022-1-1-2-211023−2300−33−33000000000000000000000000000
χ628-8-4-4044−43432-2023−23002-20000-1-11−3i321+3i3211−1+3i32−1−3i3203−33i−3i2ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000000000000
χ638-8-4-4044−43432-2023−23002-20000-1-11+3i321−3i3211−1−3i32−1+3i3203−3−3i3i−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000000000000
χ648-8-4-4044−43432-2023−2300-44000022-1-1-2-2110−2323003−33−3000000000000000000000000000
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.