Finite Group Databasebeta

← Group #13165705

Character table — Group #13165705

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222244444444668888888812121212121212121212181824242424242424242424242424242424243636363636363636363636363636727272108108108
order122236663366666644336666664412121212121212124441212121212121212121212121212121244881212121212122424242441212288
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
χ1522-2-22-2-2222-22-22-2-200222-2-2-22-200000000002-2000000000000000002i−2i00-22i2i−2i−2i20000000000
χ1622-2-22-2-2222-22-22-2-200222-2-2-22-200000000002-200000000000000000−2i2i00-2−2i−2i2i2i20000000000
χ1722-2-22-2-2222-22-22-2-200222-2-2-22-22i−2i00002i2i−2i−2i-2202i−2i0000002i2i−2i−2i0000000020000-20000000000
χ1822-2-22-2-2222-22-22-2-200222-2-2-22-2−2i2i0000−2i−2i2i2i-220−2i2i000000−2i−2i2i2i0000000020000-20000000000
χ1922-2-2-111-122-22-22-2-200-1-1-1111-112i−2i00002i2i−2i−2i-220−ii−i3i30000−i−iii−i3−i3i3i30000-10000133−3−3000000
χ2022-2-2-111-122-22-22-2-200-1-1-1111-112i−2i00002i2i−2i−2i-220−iii3−i30000−i−iiii3i3−i3−i30000-100001−3−333000000
χ2122-2-2-111-122-22-22-2-200-1-1-1111-11−2i2i0000−2i−2i2i2i-220i−i−i3i30000ii−i−i−i3−i3i3i30000-100001−3−333000000
χ2222-2-2-111-122-22-22-2-200-1-1-1111-11−2i2i0000−2i−2i2i2i-220i−ii3−i30000ii−i−ii3i3−i3−i30000-10000133−3−3000000
χ232-2-222-22-222-2-22-22-22i−2i22-22-2-2-22002i2i−2i−2i000000000002i−2i000000000000−i2i2000000−i2i2−i2i200002−2
χ242-2-222-22-222-2-22-22-22i−2i22-22-2-2-22002i2i−2i−2i000000000002i−2i000000000000i2−i2000000i2−i2i2−i20000−22
χ252-2-222-22-222-2-22-22-2−2i2i22-22-2-2-2200−2i−2i2i2i00000000000−2i2i000000000000−i2i2000000−i2i2−i2i20000−22
χ262-2-222-22-222-2-22-22-2−2i2i22-22-2-2-2200−2i−2i2i2i00000000000−2i2i000000000000i2−i2000000i2−i2i2−i200002−2
χ27444444441-21-2-211-2441-2-211-21-200-2-2-2-20000002002211-1-10000-1-1-1-1000000000000002-1-1000
χ28444444441-21-2-211-2441-2-211-21-200-2-2-2-2000000-200-2-211110000111100000000000000-211000
χ29444444441-21-2-211-2-4-41-2-211-21-200222200000020022-1-1-1-10000-1-1-1-100000000000000-211000
χ30444444441-21-2-211-2-4-41-2-211-21-2002222000000-200-2-2-1-11100001111000000000000002-1-1000
χ3144444444-21-211-2-2144-211-2-21-21221111-1-1-1-10002200-2-200-1-1-1-1000022000-1-1-1-100000000000
χ3244444444-21-211-2-2144-211-2-21-21-2-211111111000-2-200-2-20011110000-2-2000111100000000000
χ3344444444-21-211-2-21-4-4-211-2-21-2122-1-1-1-1-1-1-1-100022002200-1-1-1-10000-2-2000111100000000000
χ3444444444-21-211-2-21-4-4-211-2-21-21-2-2-1-1-1-11111000-2-20022001111000022000-1-1-1-100000000000
χ354444-2-2-2-24444444400-2-2-2-2-2-2-2-20000000000-4-40000000000000000000002000020000000000
χ3644-4-44-4-44-2121-1-22-100-21122-1-2-12i−2i3-33-3−i−iii0002i−2i000000−i−iii00002i−2i000−i−iii00000000000
χ3744-4-44-4-44-2121-1-22-100-21122-1-2-12i−2i-33-33−i−iii0002i−2i000000−i−iii0000−2i2i000ii−i−i00000000000
χ3844-4-44-4-44-2121-1-22-100-21122-1-2-1−2i2i3-33-3ii−i−i000−2i2i000000ii−i−i0000−2i2i000ii−i−i00000000000
χ3944-4-44-4-44-2121-1-22-100-21122-1-2-1−2i2i-33-33ii−i−i000−2i2i000000ii−i−i00002i−2i000−i−iii00000000000
χ4044-4-4-222-244-44-44-4-400-2-2-2222-2200000000004-400000000000000000000020000-20000000000
χ414-44-444-4-4444-4-4-4-440044-4-444-4-40000000000000000000000000000000000000000000000000
χ424-44-444-4-4-21-2-1-122100-21-12-212-1003i−3i−3i3i3−33−3000000000003−33−3000000000−i3i3−i3i300000000000
χ434-44-444-4-4-21-2-1-122100-21-12-212-1003i−3i−3i3i−33−3300000000000−33−33000000000i3−i3i3−i300000000000
χ444-44-444-4-4-21-2-1-122100-21-12-212-100−3i3i3i−3i3−33−3000000000003−33−3000000000i3−i3i3−i300000000000
χ454-44-444-4-4-21-2-1-122100-21-12-212-100−3i3i3i−3i−33−3300000000000−33−33000000000−i3i3−i3i300000000000
χ464-44-4-2-222444-4-4-4-4400-2-222-2-222000000000000000000000000000000000000000i6−i6−i6i6000000
χ474-44-4-2-222444-4-4-4-4400-2-222-2-222000000000000000000000000000000000000000−i6i6i6−i6000000
χ484-4-444-44-41-2-12-2-1124i−4i1-221-12-1-200−2i−2i2i2i00000000000i−i3−300003−33−3000000000000000−i3i3000
χ494-4-444-44-41-2-12-2-1124i−4i1-221-12-1-200−2i−2i2i2i00000000000i−i−330000−33−33000000000000000i3−i3000
χ504-4-444-44-41-2-12-2-112−4i4i1-221-12-1-2002i2i−2i−2i00000000000−ii3−300003−33−3000000000000000i3−i3000
χ514-4-444-44-41-2-12-2-112−4i4i1-221-12-1-2002i2i−2i−2i00000000000−ii−330000−33−33000000000000000−i3i3000
χ524-4-444-44-4-212-112-2-14i−4i-21-1-22-12100ii−i−i−i3i3i3−i30000000−2i2i00−i3i3i3−i3000000000−333−300000000000
χ534-4-444-44-4-212-112-2-14i−4i-21-1-22-12100ii−i−ii3−i3−i3i30000000−2i2i00i3−i3−i3i30000000003−3−3300000000000
χ544-4-444-44-4-212-112-2-1−4i4i-21-1-22-12100−i−iii−i3i3i3−i300000002i−2i00−i3i3i3−i30000000003−3−3300000000000
χ554-4-444-44-4-212-112-2-1−4i4i-21-1-22-12100−i−iiii3−i3−i3i300000002i−2i00i3−i3−i3i3000000000−333−300000000000
χ564-4-44-22-2244-4-44-44-400-2-22-2222-20000000000000000000000000000000−2i22i2000000i2−i2i2−i2000000
χ574-4-44-22-2244-4-44-44-400-2-22-2222-200000000000000000000000000000002i2−2i2000000−i2i2−i2i2000000
χ588888-4-4-4-42-42-4-422-400-122-1-12-12000000000000400-2-200-2-20000111100000000000000000000
χ598888-4-4-4-42-42-4-422-400-122-1-12-12000000000000-4002200220000-1-1-1-100000000000000000000
χ608888-4-4-4-4-42-422-4-42002-1-122-12-1440000-2-2-2-2000-2-20000001111000000000000000000000000
χ618888-4-4-4-4-42-422-4-42002-1-122-12-1-4-40000222200022000000-1-1-1-1000000000000000000000000
χ6288-8-88-8-882-4-2-442-24002-4-4-2-24240000000000000000000000000000000000000000000000000
χ6388-8-8-444-42-4-2-442-2400-12211-2-1-2000000000000000−2i32i300000000i3i3−i3−i300000000000000000000
χ6488-8-8-444-42-4-2-442-2400-12211-2-1-20000000000000002i3−2i300000000−i3−i3i3i300000000000000000000
χ6588-8-8-444-4-4242-2-44-2002-1-1-2-21214i−4i0000−2i−2i2i2i000−2i2i000000ii−i−i000000000000000000000000
χ6688-8-8-444-4-4242-2-44-2002-1-1-2-2121−4i4i00002i2i−2i−2i0002i−2i000000−i−iii000000000000000000000000
χ678-88-888-8-82-4244-2-2-4002-44-22-4-240000000000000000000000000000000000000000000000000
χ688-88-8-4-4442-4244-2-2-400-12-21-121-200000000000000000000000003i−3i−3i3i00000000000000000000
χ698-88-8-4-4442-4244-2-2-400-12-21-121-20000000000000000000000000−3i3i3i−3i00000000000000000000
χ708-88-8-4-444-42-4-2-2442002-11-22-1-2100000023−2323−2300000000000−33−33000000000000000000000000
χ718-88-8-4-444-42-4-2-2442002-11-22-1-21000000−2323−2323000000000003−33−3000000000000000000000000
χ728-8-88-44-442-4-24-4-22400-12-2-11-212000000000000000000023−230000−33−3300000000000000000000
χ738-8-88-44-442-4-24-4-22400-12-2-11-2120000000000000000000−232300003−33−300000000000000000000
χ748-8-88-44-44-424-224-4-2002-112-21-2-1000000−2i32i32i3−2i300000000000i3−i3−i3i3000000000000000000000000
χ758-8-88-44-44-424-224-4-2002-112-21-2-10000002i3−2i3−2i32i300000000000−i3i3i3−i3000000000000000000000000

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