Finite Group Databasebeta

← Group #13181157

Character table — Group #13181157

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222244444448888888888161616161616181818181818181818181818363636363636363636363636363636363636363636363636727272727272
order1234446336612121233661212121212121212121212122224881212242424242222224466688812121212242424242424666666
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1111-1-1-11-1111-1-1-111-1-1-1-1-1-1-1-1111-1-1-1
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-1-1111-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1111
χ51111-1-1111111-1-1111111-1-1-1-111-1-1-1-11-1-111111111111-111-1-1-11-1-11-1-1-1-1-1-111-1-1-1-111-111-1
χ61111-1-1111111-1-1111111-1-1-1-111-1-1-1-11-1-1111111111-1-11-1-11111-1-11-1-1111111-1-1-1-1-1-11-1-11
χ71111-1-1111111-1-1111111-1-1-1-111-1-1-1-11-1-11-1-111-1-1-1-111-1-1-11-111-1-1-111-1-111-1-1111111-1-1-11
χ81111-1-1111111-1-1111111-1-1-1-111-1-1-1-11-1-11-1-111-1-1-1-1-1-1111-11-11-1-1-11111-1-1-1-11111-1-1111-1
χ9111-11-111111-11-11111-1-111-1-1-1-111-1-1-11-11111111111-111-11-1-1-11-1-11-1-1-1-1-1-1-111-1-11-111-11
χ10111-11-111111-11-11111-1-111-1-1-1-111-1-1-11-1111111111-11-1-11-111-11-1-11-11111-1-111-1-1-11-1-11-1
χ11111-11-111111-11-11111-1-111-1-1-1-111-1-1-11-11-1-111-1-1-1-11-11-11-1-11-11-11-11-1-11111-1-1111-11-11-1
χ12111-11-111111-11-11111-1-111-1-1-1-111-1-1-11-11-1-111-1-1-1-1-11-11-111-1-11-11-1111-1-111-1-111-11-11-11
χ13111-1-1111111-1-111111-1-1-1-111-1-1-1-111-1-111111111111-1-11-1-111-1-11-1-111111-1-1-1-1111-1-11-1-1
χ14111-1-1111111-1-111111-1-1-1-111-1-1-1-111-1-11111111111-111-111-1-1-1-11-1-11-1-1-1-1-1-1-1-111-111-111
χ15111-1-1111111-1-111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11-1-1-1111-1-1-1111-111-1-11111-1-11-1-1-111
χ16111-1-1111111-1-111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1111-1-1-11-1-1111-1-1-1111111-1-1-1111-1-1
χ17222222222222222222222222222222-2-2-2-200-2-2000000000000-2-2-20000000000000000000
χ182222-2-2222222-2-2222222-2-2-2-222-2-2-2-2-222-200-2-2000000000000-2220000000000000000000
χ19222-22-222222-22-22222-2-222-2-2-2-222-2-22-22-200-2-20000000000002-220000000000000000000
χ20222-2-2222222-2-222222-2-2-2-222-2-2-2-22222-2-200-2-200000000000022-20000000000000000000
χ2122-1222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1222222-1-1-1-1-1-100000000-1-1-12220000-1-1-1-1-1-1000000
χ2222-1222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-12222-2-2-1-1111100000000-1-1-1-2-2-20000111111000000
χ2322-1222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-2-2-2-2001133−3−30000000011100000003−33−33−3000000
χ2422-1222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-2-2-2-20011−3−333000000001110000000−33−33−33000000
χ2522-12-2-2-12222-111-1-1-1-122-2-2-2-2-1-111112-2-2222-1-1-1-1-1-100000000-1112-2-20000-1-11111000000
χ2622-12-2-2-12222-111-1-1-1-122-2-2-2-2-1-111112-2-22-2-2-1-1111100000000-111-222000011-1-1-1-1000000
χ2722-12-2-2-12222-111-1-1-1-122-2-2-2-2-1-11111-222-2001133−3−3000000001-1-100000003−3−33−33000000
χ2822-12-2-2-12222-111-1-1-1-122-2-2-2-2-1-11111-222-20011−3−333000000001-1-10000000−333−33−3000000
χ2922-1-22-2-122221-11-1-1-1-1-2-222-2-211-1-1112-22-2001133−3−300000000-11-10000000−333−3−33000000
χ3022-1-22-2-122221-11-1-1-1-1-2-222-2-211-1-1112-22-20011−3−33300000000-11-100000003−3−333−3000000
χ3122-1-22-2-122221-11-1-1-1-1-2-222-2-211-1-111-22-2222-1-1-1-1-1-1000000001-11-22-2000011-1-111000000
χ3222-1-22-2-122221-11-1-1-1-1-2-222-2-211-1-111-22-22-2-2-1-11111000000001-112-220000-1-111-1-1000000
χ3322-1-2-22-1222211-1-1-1-1-1-2-2-2-2221111-1-122-2-2001133−3−300000000-1-110000000−33−333−3000000
χ3422-1-2-22-1222211-1-1-1-1-1-2-2-2-2221111-1-122-2-20011−3−33300000000-1-1100000003−33−3−33000000
χ3522-1-2-22-1222211-1-1-1-1-1-2-2-2-2221111-1-1-2-22222-1-1-1-1-1-10000000011-1-2-2200001111-1-1000000
χ3622-1-2-22-1222211-1-1-1-1-1-2-2-2-2221111-1-1-2-222-2-2-1-111110000000011-122-20000-1-1-1-111000000
χ3744444441-21-24441-21-21-21-21-21-21-21-20000000000000002220200000000-1-1000000000-1-1-1
χ3844444441-21-24441-21-21-21-21-21-21-21-2000000000000000-2-2-20-20000000011000000000111
χ394444444-21-21444-21-21-21-21-21-21-21-2100000000000022200020000000-1-100000000-1-1-1000
χ404444444-21-21444-21-21-21-21-21-21-21-21000000000000-2-2-2000-200000001100000000111000
χ414444-4-441-21-24-4-41-21-21-2-12-121-2-12-1200000000000000022-20-20000000011000000000-1-11
χ424444-4-441-21-24-4-41-21-21-2-12-121-2-12-12000000000000000-2-220200000000-1-100000000011-1
χ434444-4-44-21-214-4-4-21-21-212-12-1-212-12-100000000000022-2000-200000001100000000-1-11000
χ444444-4-44-21-214-4-4-21-21-212-12-1-212-12-1000000000000-2-2200020000000-1-10000000011-1000
χ45444-44-441-21-2-44-41-21-2-121-2-12-121-2-120000000000000002-220-20000000011000000000-11-1
χ46444-44-441-21-2-44-41-21-2-121-2-12-121-2-12000000000000000-22-20200000000-1-10000000001-11
χ47444-44-44-21-21-44-4-21-212-1-212-12-1-212-10000000000002-22000-200000001100000000-11-1000
χ48444-44-44-21-21-44-4-21-212-1-212-12-1-212-1000000000000-22-200020000000-1-1000000001-11000
χ49444-4-4441-21-2-4-441-21-2-12-121-2-12-121-20000000000000002-2-20200000000-1-1000000000-111
χ50444-4-4441-21-2-4-441-21-2-12-121-2-12-121-2000000000000000-2220-200000000110000000001-1-1
χ51444-4-444-21-21-4-44-21-212-12-1-212-12-1-210000000000002-2-200020000000-1-100000000-111000
χ52444-4-444-21-21-4-44-21-212-12-1-212-12-1-21000000000000-222000-2000000011000000001-1-1000
χ534-44000-444-4-400044-4-4000000000000000022−220022−2222−22000000000000000000000000000000
χ544-44000-444-4-400044-4-40000000000000000−222200−2222−2222000000000000000000000000000000
χ554-4-2000244-4-4000-2-222000000000000000022−2223−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000
χ564-4-2000244-4-4000-2-222000000000000000022−22−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000
χ574-4-2000244-4-4000-2-2220000000000000000−222223−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000
χ584-4-2000244-4-4000-2-2220000000000000000−2222−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ5988-4888-42-42-4-4-4-4-12-122-42-42-4-12-12-12000000000000000000000000000000000000000000
χ6088-4888-4-42-42-4-4-42-12-1-42-42-422-12-12-1000000000000000000000000000000000000000000
χ6188-48-8-8-42-42-4-444-12-122-4-24-24-121-21-2000000000000000000000000000000000000000000
χ6288-48-8-8-4-42-42-4442-12-1-424-24-22-1-21-21000000000000000000000000000000000000000000
χ6388-4-88-8-42-42-44-44-12-12-242-4-241-2-121-2000000000000000000000000000000000000000000
χ6488-4-88-8-4-42-424-442-12-14-2-424-2-212-1-21000000000000000000000000000000000000000000
χ6588-4-8-88-42-42-444-4-12-12-24-242-41-21-2-12000000000000000000000000000000000000000000
χ6688-4-8-88-4-42-4244-42-12-14-24-2-42-21-212-1000000000000000000000000000000000000000000
χ678-88000-82-4-240002-4-24000000000000000000000000000000000000000023−23000000000000
χ688-88000-82-4-240002-4-240000000000000000000000000000000000000000−2323000000000000
χ698-88000-8-424-2000-424-20000000000000000000000000000000000000023−2300000000000000
χ708-88000-8-424-2000-424-200000000000000000000000000000000000000−232300000000000000
χ7116-16-800084-8-48000-242-4000000000000000000000000000000000000000000000000000000
χ7216-16-80008-848-40004-2-42000000000000000000000000000000000000000000000000000000

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