Finite Group Databasebeta

← Group #13165516

Character table — Group #13165516

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order1222366633666666443366666644441212121212121212441212121212121212121212121212121222448812121212121224242424446688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111111111-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-111-1-1111111-1-1-1-1111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
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
χ61111111111111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111
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
χ91-11-11-11-1111-1-1-1-11i−i1111-1-1-1-1i−ii−iii−i−iii−i−i1-1i−ii−ii−ii−iii−i−iii−i−i1-11-11-1-111-1-1111-1-1i−i1-1i−i
χ101-11-11-11-1111-1-1-1-11i−i1111-1-1-1-1i−i−iiii−i−iii−i−i1-1i−i−iii−i−iiii−i−i−i−iii-111-1-11-111-1-11-1-111i−i-11−ii
χ111-11-11-11-1111-1-1-1-11i−i1111-1-1-1-1−iii−iii−i−i−i−iii1-1−iii−ii−ii−i−i−iiiii−i−i1-1-11-11-1-1-1111-1-111i−i1-1−ii
χ121-11-11-11-1111-1-1-1-11i−i1111-1-1-1-1−ii−iiii−i−i−i−iii1-1−ii−iii−i−ii−i−iii−i−iii-11-111-1-1-1-111111-1-1i−i-11i−i
χ131-11-11-11-1111-1-1-1-11−ii1111-1-1-1-1i−ii−i−i−iiiii−i−i1-1i−ii−i−iii−iii−i−iii−i−i-11-111-1-1-1-111111-1-1−ii-11−ii
χ141-11-11-11-1111-1-1-1-11−ii1111-1-1-1-1i−i−ii−i−iiiii−i−i1-1i−i−ii−ii−iiii−i−i−i−iii1-1-11-11-1-1-1111-1-111−ii1-1i−i
χ151-11-11-11-1111-1-1-1-11−ii1111-1-1-1-1−iii−i−i−iii−i−iii1-1−iii−i−iii−i−i−iiiii−i−i-111-1-11-111-1-11-1-111−ii-11i−i
χ161-11-11-11-1111-1-1-1-11−ii1111-1-1-1-1−ii−ii−i−iii−i−iii1-1−ii−ii−ii−ii−i−iii−i−iii1-11-11-1-111-1-1111-1-1−ii1-1−ii
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
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-20000222222-1-11100-2-2-1-1-1-111110000-2-2-10000-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2220000-2-2-2-22211-1-100221111-1-1-1-10000-2-2-10000-11111000000
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
χ232-22-22-22-2222-2-2-2-222i−2i2222-2-2-2-200002i2i−2i−2i0000-2200002i−2i000000000000000020000-20000−2i2i0000
χ242-22-22-22-2222-2-2-2-22−2i2i2222-2-2-2-20000−2i−2i2i2i0000-220000−2i2i000000000000000020000-200002i−2i0000
χ252-22-2-11-11222-2-2-2-2200-1-1-1-111112i−2i2i−2i00002i2i−2i−2i2-2−ii−ii002i−2i−i−iii−i−iii00002-210000-1-1-111000000
χ262-22-2-11-11222-2-2-2-2200-1-1-1-111112i−2i−2i2i00002i2i−2i−2i2-2−iii−i00−2i2i−i−iiiii−i−i0000-2210000-111-1-1000000
χ272-22-2-11-11222-2-2-2-2200-1-1-1-11111−2i2i2i−2i0000−2i−2i2i2i2-2i−i−ii002i−2iii−i−i−i−iii0000-2210000-111-1-1000000
χ282-22-2-11-11222-2-2-2-2200-1-1-1-11111−2i2i−2i2i0000−2i−2i2i2i2-2i−ii−i00−2i2iii−i−iii−i−i00002-210000-1-1-111000000
χ29444444441-2-211-2-21441-21-21-21-222001111-1-1-1-1002200-2-200-1-1-1-100000022000-1-1-1-100000000000
χ30444444441-2-211-2-21441-21-21-21-2-2-2001111111100-2-200-2-2001111000000-2-2000111100000000000
χ31444444441-2-211-2-21-4-41-21-21-21-22200-1-1-1-1-1-1-1-10022002200-1-1-1-1000000-2-2000111100000000000
χ32444444441-2-211-2-21-4-41-21-21-21-2-2-200-1-1-1-1111100-2-2002200111100000022000-1-1-1-100000000000
χ3344444444-211-2-211-244-21-21-21-210022-2-2-2-2000000002211-1-10000-1-1-1-1220000000000000000-1-100
χ3444444444-211-2-211-244-21-21-21-2100-2-2-2-2-2-200000000-2-2111100001111-2-200000000000000001100
χ3544444444-211-2-211-2-4-4-21-21-21-21002222220000000022-1-1-1-10000-1-1-1-1-2-200000000000000001100
χ3644444444-211-2-211-2-4-4-21-21-21-2100-2-2222200000000-2-2-1-11100001111220000000000000000-1-100
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-444-4-41-221-12-2-1001-2-121-2-1200003-33-33−33−300000000003−33−3000000000003−33−300000000000
χ3944-4-444-4-41-221-12-2-1001-2-121-2-1200003-33-3−33−330000000000−33−3300000000000−33−3300000000000
χ4044-4-444-4-41-221-12-2-1001-2-121-2-120000-33-333−33−300000000003−33−300000000000−33−3300000000000
χ4144-4-444-4-41-221-12-2-1001-2-121-2-120000-33-33−33−330000000000−33−33000000000003−33−300000000000
χ4244-4-444-4-444-44-4-44-40044-4-444-4-40000000000000000000000000000000000000000000000000000
χ4344-4-4-2-22244-44-4-44-400-2-222-2-222000000000000000000000000000000000000000000i6−i6i6−i6000000
χ4444-4-4-2-22244-44-4-44-400-2-222-2-222000000000000000000000000000000000000000000−i6i6−i6i6000000
χ454-44-44-44-41-2-2-1-12214i−4i1-21-2-12-122i−2i00ii−i−i−i−iii002i−2i00−2i2i00−i−iii0000002-2000-1-11100000000000
χ464-44-44-44-41-2-2-1-12214i−4i1-21-2-12-12−2i2i00ii−i−iii−i−i00−2i2i00−2i2i00ii−i−i000000-2200011-1-100000000000
χ474-44-44-44-41-2-2-1-1221−4i4i1-21-2-12-122i−2i00−i−iii−i−iii002i−2i002i−2i00−i−iii000000-2200011-1-100000000000
χ484-44-44-44-41-2-2-1-1221−4i4i1-21-2-12-12−2i2i00−i−iiiii−i−i00−2i2i002i−2i00ii−i−i0000002-2000-1-11100000000000
χ494-44-44-44-4-21122-1-1-24i−4i-21-212-12-1002i−2i−2i−2i2i2i000000002i−2ii−i−ii0000−i−iii2-20000000000000000-1100
χ504-44-44-44-4-21122-1-1-24i−4i-21-212-12-100−2i2i−2i−2i2i2i00000000−2i2ii−ii−i0000ii−i−i-2200000000000000001-100
χ514-44-44-44-4-21122-1-1-2−4i4i-21-212-12-1002i−2i2i2i−2i−2i000000002i−2i−ii−ii0000−i−iii-2200000000000000001-100
χ524-44-44-44-4-21122-1-1-2−4i4i-21-212-12-100−2i2i2i2i−2i−2i00000000−2i2i−iii−i0000ii−i−i2-20000000000000000-1100
χ534-44-4-22-22444-4-4-4-4400-2-2-2-22222000000000000-440000000000000000000000-2000020000000000
χ544-4-444-4-441-22-11-22-1001-2-12-121-200003i−3i−3i3i−i3i3i3−i30000000000−i3i3i3−i300000000000−333−300000000000
χ554-4-444-4-441-22-11-22-1001-2-12-121-200003i−3i−3i3ii3−i3−i3i30000000000i3−i3−i3i3000000000003−3−3300000000000
χ564-4-444-4-441-22-11-22-1001-2-12-121-20000−3i3i3i−3i−i3i3i3−i30000000000−i3i3i3−i3000000000003−3−3300000000000
χ574-4-444-4-441-22-11-22-1001-2-12-121-20000−3i3i3i−3ii3−i3−i3i30000000000i3−i3−i3i300000000000−333−300000000000
χ584-4-444-4-4444-4-444-4-40044-4-4-4-4440000000000000000000000000000000000000000000000000000
χ594-4-44-222-244-4-444-4-400-2-22222-2-2000000000000000000000000000000000000000000i6−i6−i6i6000000
χ604-4-44-222-244-4-444-4-400-2-22222-2-2000000000000000000000000000000000000000000−i6i6i6−i6000000
χ618888-4-4-4-42-4-422-4-4200-12-12-12-1244000000-2-2-2-200-2-2000000111100000000000000000000000000
χ628888-4-4-4-42-4-422-4-4200-12-12-12-12-4-400000022220022000000-1-1-1-100000000000000000000000000
χ638888-4-4-4-4-422-4-422-4002-12-12-12-10044000000000000-2-200-2-2000011110000000000000000000000
χ648888-4-4-4-4-422-4-422-4002-12-12-12-100-4-40000000000002200220000-1-1-1-10000000000000000000000
χ6588-8-888-8-8-42-2-44-22400-424-2-424-20000000000000000000000000000000000000000000000000000
χ6688-8-8-4-4442-442-24-4-200-121-2-121-20000000023−2323−230000000000−33−3300000000000000000000000000
χ6788-8-8-4-4442-442-24-4-200-121-2-121-200000000−2323−232300000000003−33−300000000000000000000000000
χ6888-8-8-4-444-42-2-44-224002-1-212-1-21000000000000000000000000003i−3i3i−3i0000000000000000000000
χ6988-8-8-4-444-42-2-44-224002-1-212-1-2100000000000000000000000000−3i3i−3i3i0000000000000000000000
χ708-88-8-44-442-4-4-2-244200-12-121-21-24i−4i000000−2i−2i2i2i00−2i2i000000ii−i−i00000000000000000000000000
χ718-88-8-44-442-4-4-2-244200-12-121-21-2−4i4i0000002i2i−2i−2i002i−2i000000−i−iii00000000000000000000000000
χ728-88-8-44-44-42244-2-2-4002-12-1-21-21004i−4i000000000000−2i2i00−2i2i0000ii−i−i0000000000000000000000
χ738-88-8-44-44-42244-2-2-4002-12-1-21-2100−4i4i0000000000002i−2i002i−2i0000−i−iii0000000000000000000000
χ748-8-888-8-88-42-24-42-2400-424-24-2-420000000000000000000000000000000000000000000000000000
χ758-8-88-444-42-44-22-44-200-121-21-2-1200000000−2i32i32i3−2i30000000000i3−i3−i3i300000000000000000000000000
χ768-8-88-444-42-44-22-44-200-121-21-2-12000000002i3−2i3−2i32i30000000000−i3i3i3−i300000000000000000000000000
χ778-8-88-444-4-42-24-42-24002-1-21-212-1000000000000000000000000003-3-330000000000000000000000
χ788-8-88-444-4-42-24-42-24002-1-21-212-100000000000000000000000000-333-30000000000000000000000

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