Finite Group Databasebeta

← Group #13146601

Character table — Group #13146601

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222441212121212121212121212121818181818181818242436363636363636363636363636363636363636363636363636363636363672727272
order122234466612123366666612121212444412121212121244444444888812121212121212121212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-1111-1-111111111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ611111-1-1111-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111-1-1111-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ811111-1-1111-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ91-1-111i−i-11-1i−i11-1-111-1-1ii−i−ii−i1-111-1-1i−ii−ii−i1-11-11-1i−ii−iii−i−i11-1-111-1-1ii−i−i1-1i−i
χ101-1-111i−i-11-1i−i11-1-111-1-1ii−i−ii−i1-111-1-1i−ii−i−ii1-1-11-11−iii−i−i−iii-1-111-1-111−i−iii1-1i−i
χ111-1-111i−i-11-1i−i11-1-111-1-1ii−i−ii−i1-111-1-1i−i−iii−i-111-1-11−iii−iii−i−i11-1-1-1-111−i−iii-11−ii
χ121-1-111i−i-11-1i−i11-1-111-1-1ii−i−ii−i1-111-1-1i−i−ii−ii-11-111-1i−ii−i−i−iii-1-11111-1-1ii−i−i-11−ii
χ131-1-111−ii-11-1−ii11-1-111-1-1−i−iii−ii1-111-1-1−iii−ii−i-11-111-1−ii−iiii−i−i-1-11111-1-1−i−iii-11i−i
χ141-1-111−ii-11-1−ii11-1-111-1-1−i−iii−ii1-111-1-1−iii−i−ii-111-1-11i−i−ii−i−iii11-1-1-1-111ii−i−i-11i−i
χ151-1-111−ii-11-1−ii11-1-111-1-1−i−iii−ii1-111-1-1−ii−iii−i1-1-11-11i−i−iiii−i−i-1-111-1-111ii−i−i1-1−ii
χ161-1-111−ii-11-1−ii11-1-111-1-1−i−iii−ii1-111-1-1−ii−ii−ii1-11-11-1−ii−ii−i−iii11-1-111-1-1−i−iii1-1−ii
χ17222222222222222222222222-2-2-2-2-2-2-2-222000000000000-2-200000000000000000000
χ1822222-2-2222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-20000000000002200000000000000000000
χ192-2-2222i−2i-22-22i−2i22-2-222-2-22i2i−2i−2i−2i2i-22-2-2222i−2i000000000000−2i2i00000000000000000000
χ202-2-222−2i2i-22-2−2i2i22-2-222-2-2−2i−2i2i2i2i−2i-22-2-222−2i2i0000000000002i−2i00000000000000000000
χ214444444444441-21-21-2-21-2-2-2-20000000011220022000000000000000000000000-1-1-1-1
χ224444444444441-21-21-2-21-2-2-2-20000000011-2-200-2-20000000000000000000000001111
χ23444444444444-21-21-211-2111100000000-2-200220022000000-1-1-1-1-1-1-1-1000000000000
χ24444444444444-21-21-211-2111100000000-2-200-2-200-2-200000011111111000000000000
χ2544444-4-4444-4-41-21-21-2-21222200000000-1-12200-2-200000000000000000000000011-1-1
χ2644444-4-4444-4-41-21-21-2-21222200000000-1-1-2-20022000000000000000000000000-1-111
χ2744444-4-4444-4-4-21-21-211-2-1-1-1-10000000022002200-2-2000000-1-1-1-11111000000000000
χ2844444-4-4444-4-4-21-21-211-2-1-1-1-1000000002200-2-200220000001111-1-1-1-1000000000000
χ2944-4-44004-4-40044-44-4-4-44000000000000000000000000000000000000000000000000
χ3044-4-44004-4-400-21212-1-1-23-33-30000000000000000000000003−33−33−33−3000000000000
χ3144-4-44004-4-400-21212-1-1-23-33-3000000000000000000000000−33−33−33−33000000000000
χ3244-4-44004-4-400-21212-1-1-2-33-330000000000000000000000003−33−3−33−33000000000000
χ3344-4-44004-4-400-21212-1-1-2-33-33000000000000000000000000−33−333−33−3000000000000
χ344-44-4400-4-4400444-4-4-44-4000000000000000000000000000000000000000000000000
χ354-44-4400-4-4400-21-2-12-1123i−3i−3i3i000000000000000000000000−i3i3i3−i3−333−3000000000000
χ364-44-4400-4-4400-21-2-12-1123i−3i−3i3i000000000000000000000000i3−i3−i3i33−3−33000000000000
χ374-44-4400-4-4400-21-2-12-112−3i3i3i−3i000000000000000000000000−i3i3i3−i33−3−33000000000000
χ384-44-4400-4-4400-21-2-12-112−3i3i3i−3i000000000000000000000000i3−i3−i3i3−333−3000000000000
χ394-4-4444i−4i-44-44i−4i1-2-121-22-1−2i−2i2i2i00000000i−i2i−2i002-2000000000000000000000000-11−ii
χ404-4-4444i−4i-44-44i−4i1-2-121-22-1−2i−2i2i2i00000000i−i−2i2i00-220000000000000000000000001-1i−i
χ414-4-4444i−4i-44-44i−4i-212-1-21-12ii−i−i00000000−2i2i002i−2i002-2000000−i−iii-1-111000000000000
χ424-4-4444i−4i-44-44i−4i-212-1-21-12ii−i−i00000000−2i2i00−2i2i00-22000000ii−i−i11-1-1000000000000
χ434-4-444−4i4i-44-4−4i4i1-2-121-22-12i2i−2i−2i00000000−ii2i−2i00-220000000000000000000000001-1−ii
χ444-4-444−4i4i-44-4−4i4i1-2-121-22-12i2i−2i−2i00000000−ii−2i2i002-2000000000000000000000000-11i−i
χ454-4-444−4i4i-44-4−4i4i-212-1-21-12−i−iii000000002i−2i002i−2i00-22000000−i−iii11-1-1000000000000
χ464-4-444−4i4i-44-4−4i4i-212-1-21-12−i−iii000000002i−2i00−2i2i002-2000000ii−i−i-1-111000000000000
χ476666-366-3-3-3-3-30000000000002222-1-1-1-100000000000000-1-1000000003−33−33−33−30000
χ486666-366-3-3-3-3-30000000000002222-1-1-1-100000000000000-1-100000000−33−33−33−330000
χ496666-366-3-3-3-3-3000000000000-2-2-2-21111000000000022221100000000-1-1-1-1-1-1-1-10000
χ506666-366-3-3-3-3-3000000000000-2-2-2-211110000000000-2-2-2-21100000000111111110000
χ516666-3-6-6-3-3-33300000000000022-2-21111000000000022-2-2-1-100000000-1-1-1-111110000
χ526666-3-6-6-3-3-33300000000000022-2-211110000000000-2-222-1-1000000001111-1-1-1-10000
χ536666-3-6-6-3-3-333000000000000-2-222-1-1-1-10000000000000011000000003−33−3−33−330000
χ546666-3-6-6-3-3-333000000000000-2-222-1-1-1-1000000000000001100000000−33−333−33−30000
χ556-6-66-36i−6i3-33−3i3i0000000000002i−2i2-2-1-11100000000000000−ii000000003−3−33i3−i3−i3i30000
χ566-6-66-36i−6i3-33−3i3i0000000000002i−2i2-2-1-11100000000000000−ii00000000−333−3−i3i3i3−i30000
χ576-6-66-36i−6i3-33−3i3i000000000000−2i2i-2211-1-100000000002-22i−2ii−i00000000-1-111−i−iii0000
χ586-6-66-36i−6i3-33−3i3i000000000000−2i2i-2211-1-10000000000-22−2i2ii−i0000000011-1-1ii−i−i0000
χ596-6-66-3−6i6i3-333i−3i0000000000002i−2i-2211-1-100000000002-2−2i2i−ii00000000-1-111ii−i−i0000
χ606-6-66-3−6i6i3-333i−3i0000000000002i−2i-2211-1-10000000000-222i−2i−ii0000000011-1-1−i−iii0000
χ616-6-66-3−6i6i3-333i−3i000000000000−2i2i2-2-1-11100000000000000i−i000000003−3−33−i3i3i3−i30000
χ626-6-66-3−6i6i3-333i−3i000000000000−2i2i2-2-1-11100000000000000i−i00000000−333−3i3−i3−i3i30000
χ6388-8-88008-8-8002-4-2-4-2442000000000000000000000000000000000000000000000000
χ648-88-8800-8-88002-424-24-4-2000000000000000000000000000000000000000000000000
χ651212-12-12-600-66600000000000000000023−2323−23000000000000000000000000000000000000
χ661212-12-12-600-666000000000000000000−2323−2323000000000000000000000000000000000000
χ6712-1212-12-60066-600000000000000000023−23−2323000000000000000000000000000000000000
χ6812-1212-12-60066-6000000000000000000−232323−23000000000000000000000000000000000000

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