Finite Group Databasebeta

← Group #13165518

Character table — Group #13165518

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order1222366633666666443366666644441212121212121212441212121212121212121212121212121222448812121212121224242424446688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111111111-1-11111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111
χ51111111111111111-1-1111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ91-11-11-1-111111-1-1-1-1i−i111-1-1-11-11-1i−iii−i−i11-1-1-11i−i1-1i−ii−i11-1-1ii−i−i1-1i−ii−i1ii−i−i-1ii−i−ii−i1-11-1
χ101-11-11-1-111111-1-1-1-1i−i111-1-1-11-11-1−iiii−i−i11-1-1-11−ii1-1i−i−ii11-1-1−i−iii-11i−i−ii1ii−i−i-1−i−iiii−i-11-11
χ111-11-11-1-111111-1-1-1-1i−i111-1-1-11-1-11i−iii−i−i-1-111-11i−i-11i−ii−i-1-111ii−i−i1-1−ii−ii1−i−iii-1−i−iiii−i1-1-11
χ121-11-11-1-111111-1-1-1-1i−i111-1-1-11-1-11−iiii−i−i-1-111-11−ii-11i−i−ii-1-111−i−iii-11−iii−i1−i−iii-1ii−i−ii−i-111-1
χ131-11-11-1-111111-1-1-1-1−ii111-1-1-11-11-1i−i−i−iii11-1-1-11i−i1-1−iii−i11-1-1ii−i−i-11−iii−i1−i−iii-1ii−i−i−ii-11-11
χ141-11-11-1-111111-1-1-1-1−ii111-1-1-11-11-1−ii−i−iii11-1-1-11−ii1-1−ii−ii11-1-1−i−iii1-1−ii−ii1−i−iii-1−i−iii−ii1-11-1
χ151-11-11-1-111111-1-1-1-1−ii111-1-1-11-1-11i−i−i−iii-1-111-11i−i-11−iii−i-1-111ii−i−i-11i−i−ii1ii−i−i-1−i−iii−ii-111-1
χ161-11-11-1-111111-1-1-1-1−ii111-1-1-11-1-11−ii−i−iii-1-111-11−ii-11−ii−ii-1-111−i−iii1-1i−ii−i1ii−i−i-1ii−i−i−ii1-1-11
χ1722222222222222222222222222000022220000-2-20000220000000000000000-20000-20000-2-20000
χ182222222222222222-2-2222222220000-2-2-2-20000-2-20000-2-20000000000000000-20000-20000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122220000222222-1-1-1-10022-1-1-1-1-1-1-1-1000022-10000-1-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-2000022222211-1-100-2-2-1-1-1-111110000-2-2-10000-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2220000-2-2-2-222-1-11100221111-1-1-1-10000-2-2-10000-11111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-222111100-2-211111111000022-10000-1-1-1-1-1000000
χ232-22-22-2-222222-2-2-2-22i−2i222-2-2-22-200002i2i−2i−2i00002-200002i−2i0000000000000000-2000020000−2i2i0000
χ242-22-22-2-222222-2-2-2-2−2i2i222-2-2-22-20000−2i−2i2i2i00002-20000−2i2i0000000000000000-20000200002i−2i0000
χ252-22-2-111-12222-2-2-2-200-1-1-1111-112-22i−2i000022-2-2-22−ii-11002i−2i-1-111−i−iii00002i−2i-100001−i−iii000000
χ262-22-2-111-12222-2-2-2-200-1-1-1111-112-2−2i2i000022-2-2-22i−i-1100−2i2i-1-111ii−i−i0000−2i2i-100001ii−i−i000000
χ272-22-2-111-12222-2-2-2-200-1-1-1111-11-222i−2i0000-2-222-22−ii1-1002i−2i11-1-1−i−iii0000−2i2i-100001ii−i−i000000
χ282-22-2-111-12222-2-2-2-200-1-1-1111-11-22−2i2i0000-2-222-22i−i1-100−2i2i11-1-1ii−i−i00002i−2i-100001−i−iii000000
χ29444444441-2-211-2-21441-2-211-21-222001111-1-1-1-1000022-2-200-1-1-1-100000022000-1-1-1-100000000000
χ30444444441-2-211-2-21441-2-211-21-2-2-200111111110000-2-2-2-2001111000000-2-2000111100000000000
χ31444444441-2-211-2-21-4-41-2-211-21-22200-1-1-1-1-1-1-1-10000222200-1-1-1-1000000-2-2000111100000000000
χ32444444441-2-211-2-21-4-41-2-211-21-2-2-200-1-1-1-111110000-2-22200111100000022000-1-1-1-100000000000
χ3344444444-211-2-211-244-211-2-21-210022-2-2-2-2000000220011-1-10000-1-1-1-1220000000000000000-1-100
χ3444444444-211-2-211-244-211-2-21-2100-2-2-2-2-2-2000000-2-200111100001111-2-200000000000000001100
χ3544444444-211-2-211-2-4-4-211-2-21-21002222220000002200-1-1-1-10000-1-1-1-1-2-200000000000000001100
χ3644444444-211-2-211-2-4-4-211-2-21-2100-2-22222000000-2-200-1-11100001111220000000000000000-1-100
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-444-4-41-22-112-2-1001-221-1-2-1200003-33-33−33−300000000003−33−3000000000003−33−300000000000
χ3944-4-444-4-41-22-112-2-1001-221-1-2-1200003-33-3−33−330000000000−33−3300000000000−33−3300000000000
χ4044-4-444-4-41-22-112-2-1001-221-1-2-120000-33-333−33−300000000003−33−300000000000−33−3300000000000
χ4144-4-444-4-41-22-112-2-1001-221-1-2-120000-33-33−33−330000000000−33−33000000000003−33−300000000000
χ4244-4-444-4-444-4-44-44-40044-44-44-4-40000000000000000000000000000000000000000000000000000
χ4344-4-4-2-22244-4-44-44-400-2-22-22-222000000000000000000000000000000000000000000i6−i6i6−i6000000
χ4444-4-4-2-22244-4-44-44-400-2-22-22-222000000000000000000000000000000000000000000−i6i6−i6i6000000
χ454-44-44-4-441-2-21-122-14i−4i1-2-2-1-12122-200ii−i−i-1-11100002-2−2i2i00-1-1110000002i−2i000−i−iii00000000000
χ464-44-44-4-441-2-21-122-14i−4i1-2-2-1-1212-2200ii−i−i11-1-10000-22−2i2i0011-1-1000000−2i2i000ii−i−i00000000000
χ474-44-44-4-441-2-21-122-1−4i4i1-2-2-1-12122-200−i−iii-1-11100002-22i−2i00-1-111000000−2i2i000ii−i−i00000000000
χ484-44-44-4-441-2-21-122-1−4i4i1-2-2-1-1212-2200−i−iii11-1-10000-222i−2i0011-1-10000002i−2i000−i−iii00000000000
χ494-44-44-4-44-211-22-1-124i−4i-21122-1-2-1002i−2i−2i−2i2i2i0000002i−2i00i−i−ii0000−i−iii2-20000000000000000-1100
χ504-44-44-4-44-211-22-1-124i−4i-21122-1-2-100−2i2i−2i−2i2i2i000000−2i2i00i−ii−i0000ii−i−i-2200000000000000001-100
χ514-44-44-4-44-211-22-1-12−4i4i-21122-1-2-1002i−2i2i2i−2i−2i0000002i−2i00−ii−ii0000−i−iii-2200000000000000001-100
χ524-44-44-4-44-211-22-1-12−4i4i-21122-1-2-100−2i2i2i2i−2i−2i000000−2i2i00−iii−i0000ii−i−i2-20000000000000000-1100
χ534-44-4-222-24444-4-4-4-400-2-2-2222-220000000000004-4000000000000000000000020000-20000000000
χ544-4-444-44-41-22-1-1-221001-22-112-1-200003i−3i−3i3i3−3−3300000000003−3−3300000000000i3−i3−i3i300000000000
χ554-4-444-44-41-22-1-1-221001-22-112-1-200003i−3i−3i3i−333−30000000000−333−300000000000−i3i3i3−i300000000000
χ564-4-444-44-41-22-1-1-221001-22-112-1-20000−3i3i3i−3i3−3−3300000000003−3−3300000000000−i3i3i3−i300000000000
χ574-4-444-44-41-22-1-1-221001-22-112-1-20000−3i3i3i−3i−333−30000000000−333−300000000000i3−i3−i3i300000000000
χ584-4-444-44-444-4-4-44-440044-4-44-4-440000000000000000000000000000000000000000000000000000
χ594-4-44-22-2244-4-4-44-4400-2-222-222-20000000000000000000000000000000000000000006−6−66000000
χ604-4-44-22-2244-4-4-44-4400-2-222-222-2000000000000000000000000000000000000000000−666−6000000
χ618888-4-4-4-42-4-422-4-4200-122-1-12-1244000000-2-2-2-20000-2-20000111100000000000000000000000000
χ628888-4-4-4-42-4-422-4-4200-122-1-12-12-4-400000022220000220000-1-1-1-100000000000000000000000000
χ638888-4-4-4-4-422-4-422-4002-1-122-12-100440000000000-2-20000-2-2000011110000000000000000000000
χ648888-4-4-4-4-422-4-422-4002-1-122-12-100-4-40000000000220000220000-1-1-1-10000000000000000000000
χ6588-8-888-8-8-42-24-4-22400-42-2-4424-20000000000000000000000000000000000000000000000000000
χ6688-8-8-4-4442-44-224-4-200-12-2-1121-20000000023−2323−230000000000−33−3300000000000000000000000000
χ6788-8-8-4-4442-44-224-4-200-12-2-1121-200000000−2323−232300000000003−33−300000000000000000000000000
χ6888-8-8-4-444-42-24-4-224002-112-2-1-21000000000000000000000000003i−3i3i−3i0000000000000000000000
χ6988-8-8-4-444-42-24-4-224002-112-2-1-2100000000000000000000000000−3i3i−3i3i0000000000000000000000
χ708-88-8-444-42-4-42-244-200-12211-2-1-24-4000000-2-2220000-22000011-1-100000000000000000000000000
χ718-88-8-444-42-4-42-244-200-12211-2-1-2-4400000022-2-200002-20000-1-11100000000000000000000000000
χ728-88-8-444-4-422-44-2-24002-1-1-2-2121004i−4i0000000000−2i2i0000−2i2i0000ii−i−i0000000000000000000000
χ738-88-8-444-4-422-44-2-24002-1-1-2-212100−4i4i00000000002i−2i00002i−2i0000−i−iii0000000000000000000000
χ748-8-888-88-8-42-2442-2-400-42-24-4-2420000000000000000000000000000000000000000000000000000
χ758-8-88-44-442-44-2-2-44200-12-21-1-2120000000023−23−23230000000000−333−300000000000000000000000000
χ768-8-88-44-442-44-2-2-44200-12-21-1-21200000000−232323−2300000000003−3−3300000000000000000000000000
χ778-8-88-44-44-42-2442-2-4002-11-221-2-1000000000000000000000000003-3-330000000000000000000000
χ788-8-88-44-44-42-2442-2-4002-11-221-2-100000000000000000000000000-333-30000000000000000000000

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