Finite Group Databasebeta

← Group #13146555

Character table — Group #13146555

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122241212121212121818181824363636363636363636363636363636727211222412121212121218181818243636363636363636363636363636367272
order123461233661212241212122268888242424242424242466226461266661212241212122268888242424242424242466
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111-1-1111-1-11111-1-1-1-1-1-111111111111111111-1-1111-1-11111-1-1-1-1-1-1
χ411111111111111111-1-11-1-111-1-1-1-11111-1-111111111111111111-1-11-1-111-1-1-1-11111-1-1
χ5111-11-11111-1-11-1-1-1-11-11i−ii−iii−i−iii−i−i1-1111-11-11111-1-11-1-1-1-11-11i−ii−iii−i−iii−i−i1-1
χ6111-11-11111-1-11-1-1-1-11-11−ii−ii−i−iii−i−iii1-1111-11-11111-1-11-1-1-1-11-11−ii−ii−i−iii−i−iii1-1
χ7111-11-11111-1-11-1-1-1-1-111i−i−iiii−i−i−i−iii-11111-11-11111-1-11-1-1-1-1-111i−i−iiii−i−i−i−iii-11
χ8111-11-11111-1-11-1-1-1-1-111−iii−i−i−iiiii−i−i-11111-11-11111-1-11-1-1-1-1-111−iii−i−i−iiiii−i−i-11
χ9222222222222-2-2-2-2200-200000000000000222222222222-2-2-2-2200-200000000000000
χ10222-22-22222-2-2-2222-200-200000000000000222-22-22222-2-2-2222-200-200000000000000
χ114444441-21-2110000-20002200-1-1-1-10000004444441-21-2110000-20002200-1-1-1-1000000
χ124444441-21-2110000-2000-2-20011110000004444441-21-2110000-2000-2-2001111000000
χ13444444-21-21-2-200001220000000000000-1-1444444-21-21-2-200001220000000000000-1-1
χ14444444-21-21-2-200001-2-2000000000000011444444-21-21-2-200001-2-2000000000000011
χ15444-44-41-21-2-1-1000020002i−2i00−i−iii000000444-44-41-21-2-1-1000020002i−2i00−i−iii000000
χ16444-44-41-21-2-1-100002000−2i2i00ii−i−i000000444-44-41-21-2-1-100002000−2i2i00ii−i−i000000
χ17444-44-4-21-21220000-12-20000000000000-11444-44-4-21-21220000-12-20000000000000-11
χ18444-44-4-21-21220000-1-2200000000000001-1444-44-4-21-21220000-1-2200000000000001-1
χ194-440-401-2-123i−3i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000004-440-401-2-123i−3i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ204-440-401-2-123i−3i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000004-440-401-2-123i−3i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ214-440-401-2-12−3i3i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000004-440-401-2-12−3i3i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ224-440-401-2-12−3i3i000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000004-440-401-2-12−3i3i000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ234-440-4044-4-40000000000000000000000004-440-4044-4-4000000000000000000000000
χ2466-36-3-300000022-1-1000-1000000003−33−30066-36-3-300000022-1-1000-1000000003−33−300
χ2566-36-3-300000022-1-1000-100000000−33−330066-36-3-300000022-1-1000-100000000−33−3300
χ2666-36-3-3000000-2-211000100220000-1-1-1-10066-36-3-3000000-2-211000100220000-1-1-1-100
χ2766-36-3-3000000-2-211000100-2-2000011110066-36-3-3000000-2-211000100-2-20000111100
χ2866-3-6-330000002-211000-100000000−i3i3i3−i30066-3-6-330000002-211000-100000000−i3i3i3−i300
χ2966-3-6-330000002-211000-100000000i3−i3−i3i30066-3-6-330000002-211000-100000000i3−i3−i3i300
χ3066-3-6-33000000-22-1-10001002i−2i0000−i−iii0066-3-6-33000000-22-1-10001002i−2i0000−i−iii00
χ3166-3-6-33000000-22-1-1000100−2i2i0000ii−i−i0066-3-6-33000000-22-1-1000100−2i2i0000ii−i−i00
χ328-880-80-424-20000000000000000000000008-880-80-424-2000000000000000000000000
χ3312-12-60600000000023−2300000000000000000012-12-60600000000023−23000000000000000000
χ3412-12-606000000000−232300000000000000000012-12-606000000000−2323000000000000000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ3711111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1111111
χ3811111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-111
χ39111-11-11111-1-11-1-1-1-11-11i−ii−iii−i−iii−i−i1-1-1-1-11-11-1-1-1-111-11111-11-1−ii−ii−i−iii−i−iii-11
χ40111-11-11111-1-11-1-1-1-11-11−ii−ii−i−iii−i−iii1-1-1-1-11-11-1-1-1-111-11111-11-1i−ii−iii−i−iii−i−i-11
χ41111-11-11111-1-11-1-1-1-1-111i−i−iiii−i−i−i−iii-11-1-1-11-11-1-1-1-111-111111-1-1−iii−i−i−iiiii−i−i1-1
χ42111-11-11111-1-11-1-1-1-1-111−iii−i−i−iiiii−i−i-11-1-1-11-11-1-1-1-111-111111-1-1i−i−iiii−i−i−i−iii1-1
χ43222222222222-2-2-2-2200-200000000000000-2-2-2-2-2-2-2-2-2-2-2-22222-200200000000000000
χ44222-22-22222-2-2-2222-200-200000000000000-2-2-22-22-2-2-2-2222-2-2-2200200000000000000
χ454444441-21-2110000-20002200-1-1-1-1000000-4-4-4-4-4-4-12-12-1-100002000-2-2001111000000
χ464444441-21-2110000-2000-2-2001111000000-4-4-4-4-4-4-12-12-1-1000020002200-1-1-1-1000000
χ47444444-21-21-2-200001220000000000000-1-1-4-4-4-4-4-42-12-1220000-1-2-2000000000000011
χ48444444-21-21-2-200001-2-2000000000000011-4-4-4-4-4-42-12-1220000-1220000000000000-1-1
χ49444-44-41-21-2-1-1000020002i−2i00−i−iii000000-4-4-44-44-12-12110000-2000−2i2i00ii−i−i000000
χ50444-44-41-21-2-1-100002000−2i2i00ii−i−i000000-4-4-44-44-12-12110000-20002i−2i00−i−iii000000
χ51444-44-4-21-21220000-12-20000000000000-11-4-4-44-442-12-1-2-200001-2200000000000001-1
χ52444-44-4-21-21220000-1-2200000000000001-1-4-4-44-442-12-1-2-2000012-20000000000000-11
χ534-440-401-2-123i−3i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000-44-4040-121-2−3i3i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ544-440-401-2-123i−3i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000-44-4040-121-2−3i3i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ554-440-401-2-12−3i3i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000-44-4040-121-23i−3i000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ564-440-401-2-12−3i3i000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000-44-4040-121-23i−3i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ574-440-4044-4-4000000000000000000000000-44-4040-4-444000000000000000000000000
χ5866-36-3-300000022-1-1000-1000000003−33−300-6-63-633000000-2-211000100000000−33−3300
χ5966-36-3-300000022-1-1000-100000000−33−3300-6-63-633000000-2-2110001000000003−33−300
χ6066-36-3-3000000-2-211000100220000-1-1-1-100-6-63-63300000022-1-1000-100-2-20000111100
χ6166-36-3-3000000-2-211000100-2-20000111100-6-63-63300000022-1-1000-100220000-1-1-1-100
χ6266-3-6-330000002-211000-100000000−i3i3i3−i300-6-6363-3000000-22-1-1000100000000i3−i3−i3i300
χ6366-3-6-330000002-211000-100000000i3−i3−i3i300-6-6363-3000000-22-1-1000100000000−i3i3i3−i300
χ6466-3-6-33000000-22-1-10001002i−2i0000−i−iii00-6-6363-30000002-211000-100−2i2i0000ii−i−i00
χ6566-3-6-33000000-22-1-1000100−2i2i0000ii−i−i00-6-6363-30000002-211000-1002i−2i0000−i−iii00
χ668-880-80-424-2000000000000000000000000-88-80804-2-42000000000000000000000000
χ6712-12-60600000000023−23000000000000000000-121260-6000000000−2323000000000000000000
χ6812-12-606000000000−2323000000000000000000-121260-600000000023−23000000000000000000

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