Finite Group Databasebeta

← Group #13180870

Character table — Group #13180870

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size112222244444466888899121212121616161616161616161616161616161618242436363636363636365454727272727272727272727272
order12334663612121212243612122266121233336666121212121212121246122222888824666666121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111-1-111111111111111111111-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1
χ41111111111111111111-1-111111111111111111111-111-1-111-1-111-1-1-1-111-1-1-1-1-1-111
χ51111-11111-1-1-1-1-1111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-11-11-11-1-111-11-111-1-11-11-1
χ61111-11111-1-1-1-1-1111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-11-11-11-11-11-1111-1-1-11-11
χ71111-11111-1-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-111-1-111-1-111-11-1-11-1-1111-1-11
χ81111-11111-1-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-11-1-111-1-1-111-111-1
χ9222222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122200000000220000-1-1-1-10000
χ10222222222222222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22200000000-2-2000011110000
χ112222-22222-2-2-2-2-22-1-11122-2-222-1-1-1-1-1-1-1-111111111-2-2200000000-220000-1-1110000
χ122222-22222-2-2-2-2-22-1-111-2-2-2-222-1-1-1-1-1-1-1-1111111112-22000000002-2000011-1-10000
χ13222-122-1-1-12-1-1-1222222002-12-12-1-1-12-1-1-122-1-1-1-1-1-10-1-1002200220000-1-1000000-1-1
χ14222-122-1-1-12-1-1-1222222002-12-12-1-1-12-1-1-122-1-1-1-1-1-10-1-100-2-200-2-200001100000011
χ15222-1-22-1-1-1-2111-2222-2-200-212-12-1-1-12-1-1-1-2-211111101-1002-2002-20000-11000000-11
χ16222-1-22-1-1-1-2111-2222-2-200-212-12-1-1-12-1-1-1-2-211111101-100-2200-2200001-10000001-1
χ1722-122-12-1-1-12-1-122222200-12-12-12-1-1-12-1-1-1-122-1-1-1-10-1-12200220000-1-1000000-1-100
χ1822-122-12-1-1-12-1-122222200-12-12-12-1-1-12-1-1-1-122-1-1-1-10-1-1-2-200-2-20000110000001100
χ1922-12-2-12-1-11-211-2222-2-2001-2-12-12-1-1-12-1-111-2-2111101-12-2002-20000-11000000-1100
χ2022-12-2-12-1-11-211-2222-2-2001-2-12-12-1-1-12-1-111-2-2111101-1-2200-2200001-10000001-100
χ213333333333333-1-1000033-1-1-1-100000000000000003-1-11111-1-1-1-1-1-111110000-1-1-1-1
χ223333333333333-1-1000033-1-1-1-100000000000000003-1-1-1-1-1-11111-1-1-1-1-1-100001111
χ233333333333333-1-10000-3-3-1-1-1-10000000000000000-3-1-111-1-1-1-1111111-1-10000-1-111
χ243333333333333-1-10000-3-3-1-1-1-10000000000000000-3-1-1-1-11111-1-111-1-111000011-1-1
χ253333-33333-3-3-3-31-100003311-1-10000000000000000-31-11-11-1-11-111-11-11-10000-11-11
χ263333-33333-3-3-3-31-100003311-1-10000000000000000-31-1-11-111-11-11-1-11-1100001-11-1
χ273333-33333-3-3-3-31-10000-3-311-1-1000000000000000031-11-1-11-111-1-111-1-110000-111-1
χ283333-33333-3-3-3-31-10000-3-311-1-1000000000000000031-1-111-11-1-11-11-111-100001-1-11
χ29444-244-2-2-24-2-2-244-2-2-2-2004-24-2-2111-2111-2-21111110-2-20000000000000000000000
χ30444-2-44-2-2-2-4222-44-2-22200-424-2-2111-211122-1-1-1-1-1-102-20000000000000000000000
χ3144-244-24-2-2-24-2-244-2-2-2-200-24-241-2111-21111-2-211110-2-20000000000000000000000
χ3244-24-4-24-2-22-422-44-2-222002-4-241-2111-211-1-122-1-1-1-102-20000000000000000000000
χ3344-2-24-2-211-2-21144444400-2-2-2-2-2-211-2-211-2-2-2-211110110000000000000000000000
χ3444-2-24-2-211-2-21144-2-2-2-200-2-2-2-211−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i320110000000000000000000000
χ3544-2-24-2-211-2-21144-2-2-2-200-2-2-2-211−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i320110000000000000000000000
χ3644-2-2-4-2-21122-1-1-4444-4-40022-2-2-2-211-2-2112222-1-1-1-10-110000000000000000000000
χ3744-2-2-4-2-21122-1-1-44-2-2220022-2-211−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321+3i321−3i321−3i320-110000000000000000000000
χ3844-2-2-4-2-21122-1-1-44-2-2220022-2-211−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321−3i321+3i321+3i320-110000000000000000000000
χ394-4440-4-44-40000001-13−34-400001111-1-1-1-13−33−33−33−3000000000000000001-13−30000
χ404-4440-4-44-40000001-13−3-4400001111-1-1-1-13−33−33−33−300000000000000000-11−330000
χ414-4440-4-44-40000001-1−334-400001111-1-1-1-1−33−33−33−33000000000000000001-1−330000
χ424-4440-4-44-40000001-1−33-4400001111-1-1-1-1−33−33−33−3300000000000000000-113−30000
χ434-4440-4-44-4000000-22004-40000-2-2-2-222220000000000000000000000000-22000000
χ444-4440-4-44-4000000-2200-440000-2-2-2-2222200000000000000000000000002-2000000
χ45666-366-3-3-36-3-3-3-2-2000000-21-210000000000000000011002200-2-20000-1-100000011
χ46666-366-3-3-36-3-3-3-2-2000000-21-21000000000000000001100-2-20022000011000000-1-1
χ47666-3-66-3-3-3-63332-20000002-1-2100000000000000000-11002-200-220000-110000001-1
χ48666-3-66-3-3-3-63332-20000002-1-2100000000000000000-1100-22002-200001-1000000-11
χ4966-366-36-3-3-36-3-3-2-20000001-21-200000000000000000112200-2-20000-1-10000001100
χ5066-366-36-3-3-36-3-3-2-20000001-21-20000000000000000011-2-20022000011000000-1-100
χ5166-36-6-36-3-33-6332-2000000-121-200000000000000000-112-200-220000-110000001-100
χ5266-36-6-36-3-33-6332-2000000-121-200000000000000000-11-22002-200001-1000000-1100
χ538-88-40-84-440000002-223−230000002-1-1-1-211123−23−33−33−330000000000000000000000000
χ548-88-40-84-440000002-2−23230000002-1-1-1-2111−23233−33−33−30000000000000000000000000
χ558-88-40-84-44000000-4400000000-42224-2-2-2000000000000000000000000000000000
χ568-8-4804-8-440000002-223−23000000-12-1-11-211−3323−23−33−330000000000000000000000000
χ578-8-4804-8-440000002-2−2323000000-12-1-11-2113−3−23233−33−30000000000000000000000000
χ588-8-4804-8-44000000-44000000002-422-24-2-2000000000000000000000000000000000
χ598-8-4-40442-2006i−6i002-223−23000000-1-11−3i321+3i3211−1+3i32−1−3i32−33−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ110000000000000000000000000
χ608-8-4-40442-2006i−6i002-2−2323000000-1-11+3i321−3i3211−1−3i32−1+3i323−33−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ110000000000000000000000000
χ618-8-4-40442-2006i−6i00-440000000022-1-1-2-2110000−3i3i3i−3i0000000000000000000000000
χ628-8-4-40442-200−6i6i002-223−23000000-1-11+3i321−3i3211−1−3i32−1+3i32−33−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ110000000000000000000000000
χ638-8-4-40442-200−6i6i002-2−2323000000-1-11−3i321+3i3211−1+3i32−1−3i323−33−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ110000000000000000000000000
χ648-8-4-40442-200−6i6i00-440000000022-1-1-2-21100003i−3i−3i3i0000000000000000000000000
χ651212-6-612-6-633-6-633-4-4000000222200000000000000000-1-10000000000000000000000
χ661212-6-6-12-6-63366-3-34-4000000-2-222000000000000000001-10000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.