Finite Group Databasebeta

← Group #13165520

Character table — Group #13165520

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
χ91-11-11-1-1111-11-1-11-1i−i111-1-1-11-1i−i1-1ii−i−i11-1-1-11i−i1-1i−ii−iii−i−i11-1-11-1i−ii−i1ii−i−i-1ii−i−ii−i1-11-1
χ101-11-11-1-1111-11-1-11-1i−i111-1-1-11-1i−i-11ii−i−i-1-111-11i−i-11i−ii−iii−i−i-1-1111-1−ii−ii1−i−iii-1−i−iiii−i1-1-11
χ111-11-11-1-1111-11-1-11-1i−i111-1-1-11-1−ii1-1ii−i−i11-1-1-11−ii1-1i−i−ii−i−iii11-1-1-11i−i−ii1ii−i−i-1−i−iiii−i-11-11
χ121-11-11-1-1111-11-1-11-1i−i111-1-1-11-1−ii-11ii−i−i-1-111-11−ii-11i−i−ii−i−iii-1-111-11−iii−i1−i−iii-1ii−i−ii−i-111-1
χ131-11-11-1-1111-11-1-11-1−ii111-1-1-11-1i−i1-1−i−iii11-1-1-11i−i1-1−iii−iii−i−i11-1-1-11−iii−i1−i−iii-1ii−i−i−ii-11-11
χ141-11-11-1-1111-11-1-11-1−ii111-1-1-11-1i−i-11−i−iii-1-111-11i−i-11−iii−iii−i−i-1-111-11i−i−ii1ii−i−i-1−i−iii−ii-111-1
χ151-11-11-1-1111-11-1-11-1−ii111-1-1-11-1−ii1-1−i−iii11-1-1-11−ii1-1−ii−ii−i−iii11-1-11-1−ii−ii1−i−iii-1−i−iii−ii1-11-1
χ161-11-11-1-1111-11-1-11-1−ii111-1-1-11-1−ii-11−i−iii-1-111-11−ii-11−ii−ii−i−iii-1-1111-1i−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
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-20000-2-2-2-222-1-1110022-1-1-1-111110000-2-2-10000-11111000000
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
χ232-22-22-2-2222-22-2-22-22i−2i222-2-2-22-200002i2i−2i−2i00002-200002i−2i0000000000000000-2000020000−2i2i0000
χ242-22-22-2-2222-22-2-22-2−2i2i222-2-2-22-20000−2i−2i2i2i00002-20000−2i2i0000000000000000-20000200002i−2i0000
χ252-22-2-111-122-22-2-22-200-1-1-1111-112i−2i2-2000022-2-2-22−ii-11002i−2i−i−iii-1-11100002i−2i-100001−i−iii000000
χ262-22-2-111-122-22-2-22-200-1-1-1111-112i−2i-220000-2-222-22−ii1-1002i−2i−i−iii11-1-10000−2i2i-100001ii−i−i000000
χ272-22-2-111-122-22-2-22-200-1-1-1111-11−2i2i2-2000022-2-2-22i−i-1100−2i2iii−i−i-1-1110000−2i2i-100001ii−i−i000000
χ282-22-2-111-122-22-2-22-200-1-1-1111-11−2i2i-220000-2-222-22i−i1-100−2i2iii−i−i11-1-100002i−2i-100001−i−iii000000
χ29444444441-21-2-211-2441-211-2-2-212200-2-2-2-2000000220011-1-1-1-1-1-10000220000000000000000-1-100
χ30444444441-21-2-211-2441-211-2-2-21-2-200-2-2-2-2000000-2-200111111110000-2-200000000000000001100
χ31444444441-21-2-211-2-4-41-211-2-2-21220022220000002200-1-1-1-1-1-1-1-10000-2-200000000000000001100
χ32444444441-21-2-211-2-4-41-211-2-2-21-2-2002222000000-2-200-1-11111110000220000000000000000-1-100
χ3344444444-21-211-2-2144-21-2-2111-200221111-1-1-1-1000022-2-2000000-1-1-1-10022000-1-1-1-100000000000
χ3444444444-21-211-2-2144-21-2-2111-200-2-2111111110000-2-2-2-2000000111100-2-2000111100000000000
χ3544444444-21-211-2-21-4-4-21-2-2111-20022-1-1-1-1-1-1-1-100002222000000-1-1-1-100-2-2000111100000000000
χ3644444444-21-211-2-21-4-4-21-2-2111-200-2-2-1-1-1-111110000-2-22200000011110022000-1-1-1-100000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-44-44-444-4-444-4-40044-4-44-4-440000000000000000000000000000000000000000000000000000
χ3944-4-44-44-4-212-11-22-100-21221-1-1-200003-33-33−33−3000000000000003−33−300000003−33−300000000000
χ4044-4-44-44-4-212-11-22-100-21221-1-1-200003-33-3−33−3300000000000000−33−330000000−33−3300000000000
χ4144-4-44-44-4-212-11-22-100-21221-1-1-20000-33-333−33−3000000000000003−33−30000000−33−3300000000000
χ4244-4-44-44-4-212-11-22-100-21221-1-1-20000-33-33−33−3300000000000000−33−3300000003−33−300000000000
χ4344-4-4-22-2244-4-444-4-400-2-222-222-20000000000000000000000000000000000000000006−66−6000000
χ4444-4-4-22-2244-4-444-4-400-2-222-222-2000000000000000000000000000000000000000000−66−66000000
χ454-44-44-4-441-2-1-22-1124i−4i1-21-122-2-12i−2i00−2i−2i2i2i0000002i−2i00i−i−ii−i−iii00002-20000000000000000-1100
χ464-44-44-4-441-2-1-22-1124i−4i1-21-122-2-1−2i2i00−2i−2i2i2i000000−2i2i00i−ii−iii−i−i0000-2200000000000000001-100
χ474-44-44-4-441-2-1-22-112−4i4i1-21-122-2-12i−2i002i2i−2i−2i0000002i−2i00−ii−ii−i−iii0000-2200000000000000001-100
χ484-44-44-4-441-2-1-22-112−4i4i1-21-122-2-1−2i2i002i2i−2i−2i000000−2i2i00−iii−iii−i−i00002-20000000000000000-1100
χ494-44-44-4-44-2121-12-2-14i−4i-21-22-1-112002-2ii−i−i-1-11100002-2−2i2i000000-1-111002i−2i000−i−iii00000000000
χ504-44-44-4-44-2121-12-2-14i−4i-21-22-1-11200-22ii−i−i11-1-10000-22−2i2i00000011-1-100−2i2i000ii−i−i00000000000
χ514-44-44-4-44-2121-12-2-1−4i4i-21-22-1-112002-2−i−iii-1-11100002-22i−2i000000-1-11100−2i2i000ii−i−i00000000000
χ524-44-44-4-44-2121-12-2-1−4i4i-21-22-1-11200-22−i−iii11-1-10000-222i−2i00000011-1-1002i−2i000−i−iii00000000000
χ534-44-4-222-244-44-4-44-400-2-2-2222-220000000000004-4000000000000000000000020000-20000000000
χ544-4-4444-4-4444-4-4-4-440044-44-44-4-40000000000000000000000000000000000000000000000000000
χ554-4-4444-4-4-21-2-1-122100-212-2-11-1200003i−3i−3i3i3−3−33000000000000003−3−330000000i3−i3−i3i300000000000
χ564-4-4444-4-4-21-2-1-122100-212-2-11-1200003i−3i−3i3i−333−300000000000000−333−30000000−i3i3i3−i300000000000
χ574-4-4444-4-4-21-2-1-122100-212-2-11-120000−3i3i3i−3i3−3−33000000000000003−3−330000000−i3i3i3−i300000000000
χ584-4-4444-4-4-21-2-1-122100-212-2-11-120000−3i3i3i−3i−333−300000000000000−333−30000000i3−i3−i3i300000000000
χ594-4-44-2-222444-4-4-4-4400-2-22-22-222000000000000000000000000000000000000000000i6−i6−i6i6000000
χ604-4-44-2-222444-4-4-4-4400-2-22-22-222000000000000000000000000000000000000000000−i6i6i6−i6000000
χ618888-4-4-4-42-42-4-422-400-12-1-1222-144000000000000-2-20000-2-2111100000000000000000000000000
χ628888-4-4-4-42-42-4-422-400-12-1-1222-1-4-400000000000022000022-1-1-1-100000000000000000000000000
χ638888-4-4-4-4-42-422-4-42002-122-1-1-1200440000-2-2-2-20000-2-20000000011110000000000000000000000
χ648888-4-4-4-4-42-422-4-42002-122-1-1-1200-4-40000222200002200000000-1-1-1-10000000000000000000000
χ6588-8-88-88-82-4-24-42-24002-4-2-2-44420000000000000000000000000000000000000000000000000000
χ6688-8-8-44-442-4-24-42-2400-12112-2-2-100000000000000000000003-33-300000000000000000000000000
χ6788-8-8-44-442-4-24-42-2400-12112-2-2-10000000000000000000000-33-3300000000000000000000000000
χ6888-8-8-44-44-424-22-44-2002-1-2-2-11120000000023−2323−2300000000000000−33−330000000000000000000000
χ6988-8-8-44-44-424-22-44-2002-1-2-2-111200000000−2323−2323000000000000003−33−30000000000000000000000
χ708-88-8-444-42-4-2-44-22400-12-11-2-2214i−4i000000000000−2i2i0000−2i2iii−i−i00000000000000000000000000
χ718-88-8-444-42-4-2-44-22400-12-11-2-221−4i4i0000000000002i−2i00002i−2i−i−iii00000000000000000000000000
χ728-88-8-444-4-4242-24-4-2002-12-211-1-2004-40000-2-2220000-220000000011-1-10000000000000000000000
χ738-88-8-444-4-4242-24-4-2002-12-211-1-200-44000022-2-200002-200000000-1-1110000000000000000000000
χ748-8-8888-8-82-4244-2-2-4002-4-224-44-20000000000000000000000000000000000000000000000000000
χ758-8-88-4-4442-4244-2-2-400-121-1-22-2100000000000000000000003i−3i−3i3i00000000000000000000000000
χ768-8-88-4-4442-4244-2-2-400-121-1-22-210000000000000000000000−3i3i3i−3i00000000000000000000000000
χ778-8-88-4-444-42-4-2-2442002-1-221-11-20000000023−23−232300000000000000−333−30000000000000000000000
χ788-8-88-4-444-42-4-2-2442002-1-221-11-200000000−232323−23000000000000003−3−330000000000000000000000

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