Finite Group Databasebeta

← Group #13165693

Character table — Group #13165693

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222244444444668888888812121212121212121212181824242424242424242424242424242424243636363636363636363636363636727272108108108
order1222366633666666443366666644121212121212121244412121212121212121212121212121212448812121212121224242424266288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-111-1-111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1
χ311111111111111111111111111-1-11111-1-1-1-1111-1-1111111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1111
χ51111111111111111-1-11111111111-1-1-1-111111111111-1-11111111111-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111-111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1
χ9222222222222222222222222220022220000-2-2000002200000000000000-20000-20000000-200
χ102222222222222222-2-22222222200-2-2-2-20000-2-200000-2-200000000000000-20000-20000000200
χ112222-1-1-1-12222222200-1-1-1-1-1-1-1-12200002222222-1-1-1-10022-1-1-1-1-1-1-1-10022-10000-1-1-1-1-1000000
χ122222-1-1-1-12222222200-1-1-1-1-1-1-1-1220000222222-2-1-11100-2-2-1-1-1-1111100-2-2-10000-11111000000
χ132222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-222211-1-100221111-1-1-1-100-2-2-10000-11111000000
χ142222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-222-2111100-2-2111111110022-10000-1-1-1-1-1000000
χ1522-2-222-2-22222-2-2-2-22i−2i222-2-2-22-2002i2i−2i−2i000000000002i−2i000000000000−i2i2000000−i2−i2i2i200002−2
χ1622-2-222-2-22222-2-2-2-22i−2i222-2-2-22-2002i2i−2i−2i000000000002i−2i000000000000i2−i2000000i2i2−i2−i20000−22
χ1722-2-222-2-22222-2-2-2-2−2i2i222-2-2-22-200−2i−2i2i2i00000000000−2i2i000000000000−i2i2000000−i2−i2i2i20000−22
χ1822-2-222-2-22222-2-2-2-2−2i2i222-2-2-22-200−2i−2i2i2i00000000000−2i2i000000000000i2−i2000000i2i2−i2−i200002−2
χ192-22-22-2-2222-2-222-2-20022-222-2-2-20000000000-22000000000000000002i−2i0022i2i−2i−2i-20000000000
χ202-22-22-2-2222-2-222-2-20022-222-2-2-20000000000-2200000000000000000−2i2i002−2i−2i2i2i-20000000000
χ212-22-22-2-2222-2-222-2-20022-222-2-2-22i−2i00002i2i−2i−2i2-202i−2i0000002i2i−2i−2i00000000-2000020000000000
χ222-22-22-2-2222-2-222-2-20022-222-2-2-2−2i2i0000−2i−2i2i2i2-20−2i2i000000−2i−2i2i2i00000000-2000020000000000
χ232-22-2-111-122-2-222-2-200-1-11-1-11112i−2i00002i2i−2i−2i2-20−ii3−30000−i−iii33−3−3000010000-1−i3i3−i3i3000000
χ242-22-2-111-122-2-222-2-200-1-11-1-11112i−2i00002i2i−2i−2i2-20−ii−330000−i−iii−3−333000010000-1i3−i3i3−i3000000
χ252-22-2-111-122-2-222-2-200-1-11-1-1111−2i2i0000−2i−2i2i2i2-20i−i3−30000ii−i−i33−3−3000010000-1i3−i3i3−i3000000
χ262-22-2-111-122-2-222-2-200-1-11-1-1111−2i2i0000−2i−2i2i2i2-20i−i−330000ii−i−i−3−333000010000-1−i3i3−i3i3000000
χ27444444441-2-211-2-21441-2-21-211-2221111-1-1-1-10002200-2-200-1-1-1-1000022000-1-1-1-100000000000
χ28444444441-2-211-2-21441-2-21-211-2-2-211111111000-2-200-2-20011110000-2-2000111100000000000
χ29444444441-2-211-2-21-4-41-2-21-211-222-1-1-1-1-1-1-1-100022002200-1-1-1-10000-2-2000111100000000000
χ30444444441-2-211-2-21-4-41-2-21-211-2-2-2-1-1-1-11111000-2-20022001111000022000-1-1-1-100000000000
χ3144444444-211-2-211-244-211-21-2-2100-2-2-2-20000002002211-1-10000-1-1-1-1000000000000002-1-1000
χ3244444444-211-2-211-244-211-21-2-2100-2-2-2-2000000-200-2-211110000111100000000000000-211000
χ3344444444-211-2-211-2-4-4-211-21-2-2100222200000020022-1-1-1-10000-1-1-1-100000000000000-211000
χ3444444444-211-2-211-2-4-4-211-21-2-21002222000000-200-2-2-1-11100001111000000000000002-1-1000
χ354444-2-2-2-24444444400-2-2-2-2-2-2-2-20000000000-4-40000000000000000000002000020000000000
χ3644-4-444-4-41-2-21-122-14i−4i1-2-2-12-11200ii−i−i−i3i3−i3i30000000−2i2i00−i3i3−i3i30000000003−33−300000000000
χ3744-4-444-4-41-2-21-122-14i−4i1-2-2-12-11200ii−i−ii3−i3i3−i30000000−2i2i00i3−i3i3−i3000000000−33−3300000000000
χ3844-4-444-4-41-2-21-122-1−4i4i1-2-2-12-11200−i−iii−i3i3−i3i300000002i−2i00−i3i3−i3i3000000000−33−3300000000000
χ3944-4-444-4-41-2-21-122-1−4i4i1-2-2-12-11200−i−iiii3−i3i3−i300000002i−2i00i3−i3i3−i30000000003−33−300000000000
χ4044-4-444-4-4-211-22-1-124i−4i-2112-12-2-100−2i−2i2i2i00000000000i−i3−300003−33−3000000000000000−i3i3000
χ4144-4-444-4-4-211-22-1-124i−4i-2112-12-2-100−2i−2i2i2i00000000000i−i−330000−33−33000000000000000i3−i3000
χ4244-4-444-4-4-211-22-1-12−4i4i-2112-12-2-1002i2i−2i−2i00000000000−ii3−300003−33−3000000000000000i3−i3000
χ4344-4-444-4-4-211-22-1-12−4i4i-2112-12-2-1002i2i−2i−2i00000000000−ii−330000−33−33000000000000000−i3i3000
χ4444-4-4-2-2224444-4-4-4-400-2-2-2222-220000000000000000000000000000000−2i22i2000000i2i2−i2−i2000000
χ4544-4-4-2-2224444-4-4-4-400-2-2-2222-2200000000000000000000000000000002i2−2i2000000−i2−i2i2i2000000
χ464-44-44-4-441-22-11-22-1001-221-2-1-122i−2i3-33-3−i−iii0002i−2i000000−i−iii00002i−2i000−i−iii00000000000
χ474-44-44-4-441-22-11-22-1001-221-2-1-122i−2i-33-33−i−iii0002i−2i000000−i−iii0000−2i2i000ii−i−i00000000000
χ484-44-44-4-441-22-11-22-1001-221-2-1-12−2i2i3-33-3ii−i−i000−2i2i000000ii−i−i0000−2i2i000ii−i−i00000000000
χ494-44-44-4-441-22-11-22-1001-221-2-1-12−2i2i-33-33ii−i−i000−2i2i000000ii−i−i00002i−2i000−i−iii00000000000
χ504-44-4-222-244-4-444-4-400-2-22-2-22220000000000-44000000000000000000000-2000020000000000
χ514-4-444-44-41-22-1-12-21001-22-121-1-2003i−3i−3i3i3−3−33000000000003−3−33000000000i3−i3−i3i300000000000
χ524-4-444-44-41-22-1-12-21001-22-121-1-2003i−3i−3i3i−333−300000000000−333−3000000000−i3i3i3−i300000000000
χ534-4-444-44-41-22-1-12-21001-22-121-1-200−3i3i3i−3i3−3−33000000000003−3−33000000000−i3i3i3−i300000000000
χ544-4-444-44-41-22-1-12-21001-22-121-1-200−3i3i3i−3i−333−300000000000−333−3000000000i3−i3−i3i300000000000
χ554-4-444-44-444-4-4-4-4440044-4-4-44-440000000000000000000000000000000000000000000000000
χ564-4-44-22-2244-4-4-4-44400-2-2222-22-20000000000000000000000000000000000000006−6−66000000
χ574-4-44-22-2244-4-4-4-44400-2-2222-22-2000000000000000000000000000000000000000−666−6000000
χ588888-4-4-4-42-4-422-4-4200-122-12-1-12440000-2-2-2-2000-2-20000001111000000000000000000000000
χ598888-4-4-4-42-4-422-4-4200-122-12-1-12-4-40000222200022000000-1-1-1-1000000000000000000000000
χ608888-4-4-4-4-422-4-422-4002-1-12-122-1000000000000400-2-200-2-20000111100000000000000000000
χ618888-4-4-4-4-422-4-422-4002-1-12-122-1000000000000-4002200220000-1-1-1-100000000000000000000
χ6288-8-8-4-4442-4-42-244-200-1221-21-1-2000000−2i32i3−2i32i300000000000i3−i3i3−i3000000000000000000000000
χ6388-8-8-4-4442-4-42-244-200-1221-21-1-20000002i3−2i32i3−2i300000000000−i3i3−i3i3000000000000000000000000
χ6488-8-8-4-444-422-44-2-24002-1-1-21-221000000000000000000023−230000−33−3300000000000000000000
χ6588-8-8-4-444-422-44-2-24002-1-1-21-2210000000000000000000−232300003−33−300000000000000000000
χ668-88-88-8-88-42-24-42-2400-42-2-4244-20000000000000000000000000000000000000000000000000
χ678-88-8-444-42-44-22-44-200-12-2-1211-24i−4i0000−2i−2i2i2i000−2i2i000000ii−i−i000000000000000000000000
χ688-88-8-444-42-44-22-44-200-12-2-1211-2−4i4i00002i2i−2i−2i0002i−2i000000−i−iii000000000000000000000000
χ698-88-8-444-4-42-24-42-24002-112-1-2-2100000000000000023−2300000000−3−33300000000000000000000
χ708-88-8-444-4-42-24-42-24002-112-1-2-21000000000000000−23230000000033−3−300000000000000000000
χ718-8-888-88-8-42-244-22-400-42-24-2-4420000000000000000000000000000000000000000000000000
χ728-8-88-44-442-44-2-24-4200-12-21-2-11200000023−23−232300000000000−333−3000000000000000000000000
χ738-8-88-44-442-44-2-24-4200-12-21-2-112000000−232323−23000000000003−3−33000000000000000000000000
χ748-8-88-44-44-42-244-22-4002-11-212-2-100000000000000000000000003-3-3300000000000000000000
χ758-8-88-44-44-42-244-22-4002-11-212-2-10000000000000000000000000-333-300000000000000000000

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