Finite Group Databasebeta

← Group #13146545

Character table — Group #13146545

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222441212121212121212121212121818181818181818242436363636363636363636363636363636363636363636363636363636363672727272
order122234466612123366666612121212224412121212121222444444666666888812121212242424242424242412121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ511111-1-1111-1-111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111-1-1111-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111
χ711111-1-1111-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ811111-1-1111-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ91-11-111-1-1-111-111-1-1-111-111-1-11-11-111-1-11-11-11-1i−ii−i1-111-1-1i−ii−i11-1-1ii−i−iii−i−ii−ii−i
χ101-11-111-1-1-111-111-1-1-111-111-1-11-11-111-1-11-11-11-1−ii−ii1-111-1-1−ii−ii11-1-1−i−iii−i−iii−ii−ii
χ111-11-111-1-1-111-111-1-1-111-111-1-11-11-111-1-11-1-11-11i−ii−i1-1-1-111−ii−ii-1-111−i−iii−i−iiii−ii−i
χ121-11-111-1-1-111-111-1-1-111-111-1-11-11-111-1-11-1-11-11−ii−ii1-1-1-111i−ii−i-1-111ii−i−iii−i−i−ii−ii
χ131-11-11-11-1-11-1111-1-1-111-1-1-111-111-111-1-1-111-1-11i−i−ii-1111-1-1i−i−ii-1-111ii−i−i−i−iiii−i−ii
χ141-11-11-11-1-11-1111-1-1-111-1-1-111-111-111-1-1-111-1-11−iii−i-1111-1-1−iii−i-1-111−i−iiiii−i−i−iii−i
χ151-11-11-11-1-11-1111-1-1-111-1-1-111-111-111-1-1-11-111-1i−i−ii-11-1-111−iii−i11-1-1−i−iiiii−i−ii−i−ii
χ161-11-11-11-1-11-1111-1-1-111-1-1-111-111-111-1-1-11-111-1−iii−i-11-1-111i−i−ii11-1-1ii−i−i−i−iii−iii−i
χ17222222222222222222222222-2-2-2-2-2-2-2-22200000000-2-2000000000000000000000000
χ1822222-2-2222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-20000000022000000000000000000000000
χ192-22-222-2-2-222-222-2-2-222-222-2-2-22-22-2-2222-200000000-22000000000000000000000000
χ202-22-22-22-2-22-2222-2-2-222-2-2-2222-2-22-2-222-22000000002-2000000000000000000000000
χ214444444444441-21-2-21-21-2-2-2-20000000011000022220000000000000000000000-1-1-1-1
χ224444444444441-21-2-21-21-2-2-2-200000000110000-2-2-2-200000000000000000000001111
χ23444444444444-21-211-21-2111100000000-2-22222000000-1-1-1-10000-1-1-1-1000000000000
χ24444444444444-21-211-21-2111100000000-2-2-2-2-2-2000000111100001111000000000000
χ2544444-4-4444-4-41-21-2-21-21222200000000-1-1000022-2-20000000000000000000000-1-111
χ2644444-4-4444-4-41-21-2-21-21222200000000-1-10000-2-222000000000000000000000011-1-1
χ2744444-4-4444-4-4-21-211-21-2-1-1-1-1000000002222-2-2000000-1-1-1-100001111000000000000
χ2844444-4-4444-4-4-21-211-21-2-1-1-1-10000000022-2-22200000011110000-1-1-1-1000000000000
χ2944-4-44004-4-4004444-4-4-4-4000000000000000000000000000000000000000000000000
χ3044-4-44004-4-400-21-21-12-123i−3i3i−3i00000000000000000000−i3i3−i3i300003−33−3000000000000
χ3144-4-44004-4-400-21-21-12-123i−3i3i−3i00000000000000000000i3−i3i3−i30000−33−33000000000000
χ3244-4-44004-4-400-21-21-12-12−3i3i−3i3i00000000000000000000−i3i3−i3i30000−33−33000000000000
χ3344-4-44004-4-400-21-21-12-12−3i3i−3i3i00000000000000000000i3−i3i3−i300003−33−3000000000000
χ344-44-444-4-4-444-41-2-1221-2-1-2-222000000001-100002i−2i2i−2i0000000000000000000000−ii−ii
χ354-44-444-4-4-444-41-2-1221-2-1-2-222000000001-10000−2i2i−2i2i0000000000000000000000i−ii−i
χ364-44-444-4-4-444-4-212-1-1-21211-1-100000000-222-22-2000000-1-1110000-1-111000000000000
χ374-44-444-4-4-444-4-212-1-1-21211-1-100000000-22-22-2200000011-1-1000011-1-1000000000000
χ384-44-44-44-4-44-441-2-1221-2-122-2-200000000-1100002i−2i−2i2i0000000000000000000000−iii−i
χ394-44-44-44-4-44-441-2-1221-2-122-2-200000000-110000−2i2i2i−2i0000000000000000000000i−i−ii
χ404-44-44-44-4-44-44-212-1-1-212-1-111000000002-22-2-22000000-1-111000011-1-1000000000000
χ414-44-44-44-4-44-44-212-1-1-212-1-111000000002-2-222-200000011-1-10000-1-111000000000000
χ424-4-44400-44-40044-4-44-4-44000000000000000000000000000000000000000000000000
χ434-4-44400-44-400-212-112-1-23i−3i−3i3i00000000000000000000−i3i3i3−i300003−3−33000000000000
χ444-4-44400-44-400-212-112-1-23i−3i−3i3i00000000000000000000i3−i3−i3i30000−333−3000000000000
χ454-4-44400-44-400-212-112-1-2−3i3i3i−3i00000000000000000000−i3i3i3−i30000−333−3000000000000
χ464-4-44400-44-400-212-112-1-2−3i3i3i−3i00000000000000000000i3−i3−i3i300003−3−33000000000000
χ476666-366-3-3-3-3-30000000000002222-1-1-1-10000000000-1-10000000000003−33−33−33−30000
χ486666-366-3-3-3-3-30000000000002222-1-1-1-10000000000-1-1000000000000−33−33−33−330000
χ496666-366-3-3-3-3-3000000000000-2-2-2-21111000000000011000022220000-1-1-1-1-1-1-1-10000
χ506666-366-3-3-3-3-3000000000000-2-2-2-211110000000000110000-2-2-2-20000111111110000
χ516666-3-6-6-3-3-33300000000000022-2-211110000000000-1-1000022-2-20000-1-1-1-111110000
χ526666-3-6-6-3-3-33300000000000022-2-211110000000000-1-10000-2-22200001111-1-1-1-10000
χ536666-3-6-6-3-3-333000000000000-2-222-1-1-1-10000000000110000000000003−33−3−33−330000
χ546666-3-6-6-3-3-333000000000000-2-222-1-1-1-1000000000011000000000000−33−333−33−30000
χ556-66-6-36-633-3-330000000000002-22-2-1-1110000000000-11000000000000−i3i3i3−i3−i3i3i3−i30000
χ566-66-6-36-633-3-330000000000002-22-2-1-1110000000000-11000000000000i3−i3−i3i3i3−i3−i3i30000
χ576-66-6-36-633-3-33000000000000-22-2211-1-100000000001-100002i−2i2i−2i0000−i−iii−i−iii0000
χ586-66-6-36-633-3-33000000000000-22-2211-1-100000000001-10000−2i2i−2i2i0000ii−i−iii−i−i0000
χ596-66-6-3-6633-33-30000000000002-2-2211-1-10000000000-1100002i−2i−2i2i0000−i−iiiii−i−i0000
χ606-66-6-3-6633-33-30000000000002-2-2211-1-10000000000-110000−2i2i2i−2i0000ii−i−i−i−iii0000
χ616-66-6-3-6633-33-3000000000000-222-2-1-11100000000001-1000000000000−i3i3i3−i3i3−i3−i3i30000
χ626-66-6-3-6633-33-3000000000000-222-2-1-11100000000001-1000000000000i3−i3−i3i3−i3i3i3−i30000
χ6388-8-88008-8-8002-42-44-24-2000000000000000000000000000000000000000000000000
χ648-8-88800-88-8002-4-24-4-242000000000000000000000000000000000000000000000000
χ651212-12-12-600-66600000000000000000023−2323−23000000000000000000000000000000000000
χ661212-12-12-600-666000000000000000000−2323−2323000000000000000000000000000000000000
χ6712-12-1212-6006-6600000000000000000023−23−2323000000000000000000000000000000000000
χ6812-12-1212-6006-66000000000000000000−232323−23000000000000000000000000000000000000

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