Finite Group Databasebeta

← Group #13165522

Character table — Group #13165522

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order122236663366666644336666664444121212121212121244121212121212121212121212121212124444881212121212122424242444121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
χ311111111111111111111111111-1-1111111111111-1-11111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-1-1
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
χ61111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111
χ71111111111111111-1-111111111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11-1-1-1-1-1-11111
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
χ91-1-111-1-1111-1-1-1-111i−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
χ101-1-111-1-1111-1-1-1-111i−i1111-1-1-1-1i−i−iiii−i−i−i−iii1-1i−i−iii−ii−iii−i−i−i−iii1-1-11-11-1-1-1111-1-111i−i1-1−ii
χ111-1-111-1-1111-1-1-1-111i−i1111-1-1-1-1−iii−iii−i−iii−i−i1-1−iii−ii−i−ii−i−iiiii−i−i-111-1-11-111-1-11-1-111i−i-11−ii
χ121-1-111-1-1111-1-1-1-111i−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
χ131-1-111-1-1111-1-1-1-111−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
χ141-1-111-1-1111-1-1-1-111−ii1111-1-1-1-1i−i−ii−i−iii−i−iii1-1i−i−ii−iii−iii−i−i−i−iii-111-1-11-111-1-11-1-111−ii-11i−i
χ151-1-111-1-1111-1-1-1-111−ii1111-1-1-1-1−iii−i−i−iiiii−i−i1-1−iii−i−ii−ii−i−iiiii−i−i1-1-11-11-1-1-1111-1-111−ii1-1i−i
χ161-1-111-1-1111-1-1-1-111−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
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-20000-2-2-2-222-1-1110022-1-1-1-111110000-2-2-10000-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-222000022222211-1-100-2-21111-1-1-1-10000-2-2-10000-11111000000
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
χ232-2-222-2-2222-2-2-2-2222i−2i2222-2-2-2-200002i2i−2i−2i0000-2200002i−2i000000000000000020000-20000−2i2i0000
χ242-2-222-2-2222-2-2-2-222−2i2i2222-2-2-2-20000−2i−2i2i2i0000-220000−2i2i000000000000000020000-200002i−2i0000
χ252-2-22-111-122-2-2-2-22200-1-1-1-111112i−2i2i−2i00002i2i−2i−2i2-2−ii−ii002i−2i−i−iii−i−iii00002-210000-1-1-111000000
χ262-2-22-111-122-2-2-2-22200-1-1-1-111112i−2i−2i2i0000−2i−2i2i2i2-2−iii−i002i−2i−i−iiiii−i−i0000-2210000-111-1-1000000
χ272-2-22-111-122-2-2-2-22200-1-1-1-11111−2i2i2i−2i00002i2i−2i−2i2-2i−i−ii00−2i2iii−i−i−i−iii0000-2210000-111-1-1000000
χ282-2-22-111-122-2-2-2-22200-1-1-1-11111−2i2i−2i2i0000−2i−2i2i2i2-2i−ii−i00−2i2iii−i−iii−i−i00002-210000-1-1-111000000
χ29444444441-21-2-211-2441-21-21-21-22200-2-2-2-2000000220011-1-1-1-1-1-10000220000000000000000-1-100
χ30444444441-21-2-211-2441-21-21-21-2-2-200-2-2-2-2000000-2-200111111110000-2-200000000000000001100
χ31444444441-21-2-211-2-4-41-21-21-21-2220022220000002200-1-1-1-1-1-1-1-10000-2-200000000000000001100
χ32444444441-21-2-211-2-4-41-21-21-21-2-2-2002222000000-2-200-1-11111110000220000000000000000-1-100
χ3344444444-21-211-2-2144-21-21-21-2100221111-1-1-1-1000022-2-2000000-1-1-1-10022000-1-1-1-100000000000
χ3444444444-21-211-2-2144-21-21-21-2100-2-2111111110000-2-2-2-2000000111100-2-2000111100000000000
χ3544444444-21-211-2-21-4-4-21-21-21-210022-1-1-1-1-1-1-1-100002222000000-1-1-1-100-2-2000111100000000000
χ3644444444-21-211-2-21-4-4-21-21-21-2100-2-2-1-1-1-111110000-2-22200000011110022000-1-1-1-100000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-444-4-444-44-44-4-40044-4-4-444-40000000000000000000000000000000000000000000000000000
χ3944-4-444-4-4-2121-1-22-100-212-121-2-100003-33-33−33−3000000000000003−33−300000003−33−300000000000
χ4044-4-444-4-4-2121-1-22-100-212-121-2-100003-33-3−33−3300000000000000−33−330000000−33−3300000000000
χ4144-4-444-4-4-2121-1-22-100-212-121-2-10000-33-333−33−3000000000000003−33−30000000−33−3300000000000
χ4244-4-444-4-4-2121-1-22-100-212-121-2-10000-33-33−33−3300000000000000−33−3300000003−33−300000000000
χ4344-4-4-2-22244-44-44-4-400-2-2222-2-220000000000000000000000000000000000000000006−66−6000000
χ4444-4-4-2-22244-44-44-4-400-2-2222-2-22000000000000000000000000000000000000000000−66−66000000
χ454-44-44-44-4444-44-4-4-40044-4-44-4-440000000000000000000000000000000000000000000000000000
χ464-44-44-44-4-21-2-1122-100-212-1-2-12100003i−3i−3i3i−i3i3i3−i300000000000000−i3i3i3−i30000000−333−300000000000
χ474-44-44-44-4-21-2-1122-100-212-1-2-12100003i−3i−3i3ii3−i3−i3i300000000000000i3−i3−i3i300000003−3−3300000000000
χ484-44-44-44-4-21-2-1122-100-212-1-2-1210000−3i3i3i−3i−i3i3i3−i300000000000000−i3i3i3−i300000003−3−3300000000000
χ494-44-44-44-4-21-2-1122-100-212-1-2-1210000−3i3i3i−3ii3−i3−i3i300000000000000i3−i3−i3i30000000−333−300000000000
χ504-44-4-22-22444-44-4-4-400-2-222-222-20000000000000000000000000000000000000000006−6−66000000
χ514-44-4-22-22444-44-4-4-400-2-222-222-2000000000000000000000000000000000000000000−666−6000000
χ524-4-444-4-441-2-122-11-24i−4i1-21-2-12-122i−2i00−2i−2i2i2i0000002i−2i00i−i−ii−i−iii00002-20000000000000000-1100
χ534-4-444-4-441-2-122-11-24i−4i1-21-2-12-12−2i2i00−2i−2i2i2i000000−2i2i00i−ii−iii−i−i0000-2200000000000000001-100
χ544-4-444-4-441-2-122-11-2−4i4i1-21-2-12-122i−2i002i2i−2i−2i0000002i−2i00−ii−ii−i−iii0000-2200000000000000001-100
χ554-4-444-4-441-2-122-11-2−4i4i1-21-2-12-12−2i2i002i2i−2i−2i000000−2i2i00−iii−iii−i−i00002-20000000000000000-1100
χ564-4-444-4-44-212-1-12-214i−4i-21-212-12-1002i−2iii−i−i−i−iii00002i−2i−2i2i000000−i−iii002-2000-1-11100000000000
χ574-4-444-4-44-212-1-12-214i−4i-21-212-12-100−2i2iii−i−iii−i−i0000−2i2i−2i2i000000ii−i−i00-2200011-1-100000000000
χ584-4-444-4-44-212-1-12-21−4i4i-21-212-12-1002i−2i−i−iii−i−iii00002i−2i2i−2i000000−i−iii00-2200011-1-100000000000
χ594-4-444-4-44-212-1-12-21−4i4i-21-212-12-100−2i2i−i−iiiii−i−i0000−2i2i2i−2i000000ii−i−i002-2000-1-11100000000000
χ604-4-44-222-244-4-4-4-44400-2-2-2-22222000000000000-440000000000000000000000-2000020000000000
χ618888-4-4-4-42-42-4-422-400-12-12-12-1244000000000000-2-20000-2-2111100000000000000000000000000
χ628888-4-4-4-42-42-4-422-400-12-12-12-12-4-400000000000022000022-1-1-1-100000000000000000000000000
χ638888-4-4-4-4-42-422-4-42002-12-12-12-100440000-2-2-2-20000-2-20000000011110000000000000000000000
χ648888-4-4-4-4-42-422-4-42002-12-12-12-100-4-40000222200002200000000-1-1-1-10000000000000000000000
χ6588-8-888-8-82-4-2-442-24002-4-24-2-4240000000000000000000000000000000000000000000000000000
χ6688-8-8-4-4442-4-2-442-2400-121-212-1-200000000000000000000003-33-300000000000000000000000000
χ6788-8-8-4-4442-4-2-442-2400-121-212-1-20000000000000000000000-33-3300000000000000000000000000
χ6888-8-8-4-444-4242-2-44-2002-1-21-2-1210000000023−2323−2300000000000000−33−330000000000000000000000
χ6988-8-8-4-444-4242-2-44-2002-1-21-2-12100000000−2323−2323000000000000003−33−30000000000000000000000
χ708-88-88-88-82-424-4-2-24002-4-2424-2-40000000000000000000000000000000000000000000000000000
χ718-88-8-44-442-424-4-2-2400-121-2-1-21200000000000000000000003i−3i−3i3i00000000000000000000000000
χ728-88-8-44-442-424-4-2-2400-121-2-1-2120000000000000000000000−3i3i3i−3i00000000000000000000000000
χ738-88-8-44-44-42-4-2244-2002-1-2121-2-100000000−2i32i32i3−2i300000000000000i3−i3−i3i30000000000000000000000
χ748-88-8-44-44-42-4-2244-2002-1-2121-2-1000000002i3−2i3−2i32i300000000000000−i3i3i3−i30000000000000000000000
χ758-8-88-444-42-4-244-22-400-12-121-21-24i−4i000000000000−2i2i0000−2i2iii−i−i00000000000000000000000000
χ768-8-88-444-42-4-244-22-400-12-121-21-2−4i4i0000000000002i−2i00002i−2i−i−iii00000000000000000000000000
χ778-8-88-444-4-424-2-24-42002-12-1-21-21004i−4i0000−2i−2i2i2i0000−2i2i00000000ii−i−i0000000000000000000000
χ788-8-88-444-4-424-2-24-42002-12-1-21-2100−4i4i00002i2i−2i−2i00002i−2i00000000−i−iii0000000000000000000000

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