Finite Group Databasebeta

← Group #13146612

Character table — Group #13146612

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244999912121212121212121212121218181818181818181818181818182424363636363636363636363636363636363636363636363636363672727272
order12223446661212222233666666121212124444444444666612124444444412121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-1111-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ611111-1-1111-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ711111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ811111-1-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ91-1-111i−i1-1-1i−i1-11-111-1-111-1-1ii−i−iii−i−ii−i11-1-11-11-1i−ii−i1-11-1i−ii−iii−i−i11-1-111-1-1ii−i−i1-1i−i
χ101-1-111i−i1-1-1i−i1-11-111-1-111-1-1ii−i−iii−i−ii−i11-1-11-11-1i−i−ii-11-11−iii−iii−i−i11-1-1-1-111−i−iii-11−ii
χ111-1-111i−i1-1-1i−i1-11-111-1-111-1-1ii−i−i−i−iiii−i-1-1111-11-1i−ii−i1-1-11−iii−i−i−iii-1-111-1-111−i−iii1-1i−i
χ121-1-111i−i1-1-1i−i1-11-111-1-111-1-1ii−i−i−i−iiii−i-1-1111-11-1i−i−ii-111-1i−ii−i−i−iii-1-11111-1-1ii−i−i-11−ii
χ131-1-111−ii1-1-1−ii1-11-111-1-111-1-1−i−iiiii−i−i−ii-1-1111-11-1−iii−i-111-1−ii−iiii−i−i-1-11111-1-1−i−iii-11i−i
χ141-1-111−ii1-1-1−ii1-11-111-1-111-1-1−i−iiiii−i−i−ii-1-1111-11-1−ii−ii1-1-11i−i−iiii−i−i-1-111-1-111ii−i−i1-1−ii
χ151-1-111−ii1-1-1−ii1-11-111-1-111-1-1−i−iii−i−iii−ii11-1-11-11-1−iii−i-11-11i−i−ii−i−iii11-1-1-1-111ii−i−i-11i−i
χ161-1-111−ii1-1-1−ii1-11-111-1-111-1-1−i−iii−i−iii−ii11-1-11-11-1−ii−ii1-11-1−ii−ii−i−iii11-1-111-1-1−i−iii1-1−ii
χ17222222222222-2-2-2-22222222222220000-2-20000-2-2-2-22200000000-2-200000000000000000000
χ1822222-2-2222-2-2-2-2-2-222222222-2-2-2-20000220000-2-2-2-2-2-2000000002200000000000000000000
χ1922-2-2200-22-20022-2-2222-2-2-22-200002-22-200000022-2-20000000000002-22-20000000000000000
χ2022-2-2200-22-20022-2-2222-2-2-22-20000-22-2200000022-2-2000000000000-22-220000000000000000
χ2122-2-2200-22-200-2-222222-2-2-22-200000000002i−2i2i−2i-2-22200000000000000002i−2i2i−2i000000000000
χ2222-2-2200-22-200-2-222222-2-2-22-20000000000−2i2i−2i2i-2-2220000000000000000−2i2i−2i2i000000000000
χ232-22-2200-2-22002-2-2222-22-2-2-2200002i−2i−2i2i0000002-2-220000000000002i−2i−2i2i0000000000000000
χ242-22-2200-2-22002-2-2222-22-2-2-220000−2i2i2i−2i0000002-2-22000000000000−2i2i2i−2i0000000000000000
χ252-22-2200-2-2200-222-222-22-2-2-2200000000002i−2i−2i2i-222-200000000000000002i−2i−2i2i000000000000
χ262-22-2200-2-2200-222-222-22-2-2-220000000000−2i2i2i−2i-222-20000000000000000−2i2i2i−2i000000000000
χ272-2-2222i−2i2-2-22i−2i-22-2222-2-222-2-22i2i−2i−2i0000−2i2i0000-22-222i−2i00000000−2i2i00000000000000000000
χ282-2-222−2i2i2-2-2−2i2i-22-2222-2-222-2-2−2i−2i2i2i00002i−2i0000-22-22−2i2i000000002i−2i00000000000000000000
χ2944444444444400001-21-21-2-21-2-2-2-2000000000000001122220000000000000000000000-1-1-1-1
χ3044444444444400001-21-21-2-21-2-2-2-20000000000000011-2-2-2-200000000000000000000001111
χ314444444444440000-21-21-211-2111122220022220000-2-20000000000-1-1-1-1-1-1-1-1000000000000
χ324444444444440000-21-21-211-21111-2-2-2-200-2-2-2-20000-2-2000000000011111111000000000000
χ3344444-4-4444-4-400001-21-21-2-21222200000000000000-1-122-2-2000000000000000000000011-1-1
χ3444444-4-4444-4-400001-21-21-2-21222200000000000000-1-1-2-2220000000000000000000000-1-111
χ3544444-4-4444-4-40000-21-21-211-2-1-1-1-1222200-2-2-2-20000220000000000-1-1-1-11111000000000000
χ3644444-4-4444-4-40000-21-21-211-2-1-1-1-1-2-2-2-200222200002200000000001111-1-1-1-1000000000000
χ3744-4-4400-44-4000000-21-2-12-1123i−3i3i−3i2-22-2002i−2i2i−2i0000000000000000-11-11−ii−ii000000000000
χ3844-4-4400-44-4000000-21-2-12-1123i−3i3i−3i-22-2200−2i2i−2i2i00000000000000001-11-1i−ii−i000000000000
χ3944-4-4400-44-4000000-21-2-12-112−3i3i−3i3i2-22-200−2i2i−2i2i0000000000000000-11-11i−ii−i000000000000
χ4044-4-4400-44-4000000-21-2-12-112−3i3i−3i3i-22-22002i−2i2i−2i00000000000000001-11-1−ii−ii000000000000
χ414-44-4400-4-44000000-21212-1-1-23-3-332i−2i−2i2i00−2i2i2i−2i0000000000000000−iii−ii−i−ii000000000000
χ424-44-4400-4-44000000-21212-1-1-23-3-33−2i2i2i−2i002i−2i−2i2i0000000000000000i−i−ii−iii−i000000000000
χ434-44-4400-4-44000000-21212-1-1-2-333-32i−2i−2i2i002i−2i−2i2i0000000000000000−iii−i−iii−i000000000000
χ444-44-4400-4-44000000-21212-1-1-2-333-3−2i2i2i−2i00−2i2i2i−2i0000000000000000i−i−iii−i−ii000000000000
χ454-4-4444i−4i4-4-44i−4i00001-2-121-22-1−2i−2i2i2i00000000000000i−i2i−2i2-20000000000000000000000-11−ii
χ464-4-4444i−4i4-4-44i−4i00001-2-121-22-1−2i−2i2i2i00000000000000i−i−2i2i-2200000000000000000000001-1i−i
χ474-4-4444i−4i4-4-44i−4i0000-212-1-21-12ii−i−i2i2i−2i−2i0022-2-20000−2i2i0000000000−i−iii-1-111000000000000
χ484-4-4444i−4i4-4-44i−4i0000-212-1-21-12ii−i−i−2i−2i2i2i00-2-2220000−2i2i0000000000ii−i−i11-1-1000000000000
χ494-4-444−4i4i4-4-4−4i4i00001-2-121-22-12i2i−2i−2i00000000000000−ii2i−2i-2200000000000000000000001-1−ii
χ504-4-444−4i4i4-4-4−4i4i00001-2-121-22-12i2i−2i−2i00000000000000−ii−2i2i2-20000000000000000000000-11i−i
χ514-4-444−4i4i4-4-4−4i4i0000-212-1-21-12−i−iii2i2i−2i−2i00-2-22200002i−2i0000000000−i−iii11-1-1000000000000
χ524-4-444−4i4i4-4-4−4i4i0000-212-1-21-12−i−iii−2i−2i2i2i0022-2-200002i−2i0000000000ii−i−i-1-111000000000000
χ536666-366-3-3-3-3-322220000000000000000220000-1-1-1-10000000000-1-1000000003−33−33−33−30000
χ546666-366-3-3-3-3-322220000000000000000220000-1-1-1-10000000000-1-100000000−33−33−33−330000
χ556666-366-3-3-3-3-3-2-2-2-20000000000000000-2-20000111100000022221100000000-1-1-1-1-1-1-1-10000
χ566666-366-3-3-3-3-3-2-2-2-20000000000000000-2-200001111000000-2-2-2-21100000000111111110000
χ576666-3-6-6-3-3-33322220000000000000000-2-20000-1-1-1-1000000000011000000003−33−3−33−330000
χ586666-3-6-6-3-3-33322220000000000000000-2-20000-1-1-1-100000000001100000000−33−333−33−30000
χ596666-3-6-6-3-3-333-2-2-2-20000000000000000220000111100000022-2-2-1-100000000-1-1-1-111110000
χ606666-3-6-6-3-3-333-2-2-2-200000000000000002200001111000000-2-222-1-1000000001111-1-1-1-10000
χ616-6-66-36i−6i-333−3i3i2-22-200000000000000002i−2i0000-11-110000000000−ii000000003−3−33i3−i3−i3i30000
χ626-6-66-36i−6i-333−3i3i2-22-200000000000000002i−2i0000-11-110000000000−ii00000000−333−3−i3i3i3−i30000
χ636-6-66-36i−6i-333−3i3i-22-220000000000000000−2i2i00001-11-10000002-22i−2ii−i00000000-1-111−i−iii0000
χ646-6-66-36i−6i-333−3i3i-22-220000000000000000−2i2i00001-11-1000000-22−2i2ii−i0000000011-1-1ii−i−i0000
χ656-6-66-3−6i6i-3333i−3i2-22-20000000000000000−2i2i0000-11-110000000000i−i000000003−3−33−i3i3i3−i30000
χ666-6-66-3−6i6i-3333i−3i2-22-20000000000000000−2i2i0000-11-110000000000i−i00000000−333−3i3−i3−i3i30000
χ676-6-66-3−6i6i-3333i−3i-22-2200000000000000002i−2i00001-11-10000002-2−2i2i−ii00000000-1-111ii−i−i0000
χ686-6-66-3−6i6i-3333i−3i-22-2200000000000000002i−2i00001-11-1000000-222i−2i−ii0000000011-1-1−i−iii0000
χ6988-8-8800-88-80000002-424-24-4-200000000000000000000000000000000000000000000000000
χ708-88-8800-8-880000002-4-2-4-244200000000000000000000000000000000000000000000000000
χ711212-12-12-6006-660044-4-40000000000000000000000-2-22200000000000000000000000000000000
χ721212-12-12-6006-6600-4-444000000000000000000000022-2-200000000000000000000000000000000
χ7312-1212-12-60066-6004-4-440000000000000000000000-222-200000000000000000000000000000000
χ7412-1212-12-60066-600-444-400000000000000000000002-2-2200000000000000000000000000000000

Here i is the imaginary unit (i² = −1).