Finite Group Databasebeta

← Group #10590141

Character table — Group #10590141

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11222222244444444444444444444444444444444991818181818181872727272
order124881616161633661212121224242424242424244848484848484848484848484848484844288161616168888
χ1111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1ii−i−i
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1−i−iii
χ511111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-11-1
χ611111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-11
χ711111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−i−ii
χ811111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−iii−i
χ9222-2-2000022222222-2-2-2-2-2-2-2-20000000000000000222-2-200000000
χ10222-2-2000022222222-2-2-2-2-2-2-2-20000000000000000-2-2-22200000000
χ1122-20022−2−22222-2-2-2-20000000022222222−2−2−2−2−2−2−2−222-20022−2−20000
χ1222-20022−2−22222-2-2-2-20000000022222222−2−2−2−2−2−2−2−2-2-2200−2−2220000
χ1322-200−2−2222222-2-2-2-200000000−2−2−2−2−2−2−2−22222222222-200−2−2220000
χ1422-200−2−2222222-2-2-2-200000000−2−2−2−2−2−2−2−222222222-2-220022−2−20000
χ152-202−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ522-2-200002222−2−2−2−2ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ52i−2i0i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ162-202−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ522-2-200002222−2−2−2−2ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−2i2i0−i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ172-202−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ522-2-200002222−2−2−2−2−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ52i−2i0i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ182-202−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ522-2-200002222−2−2−2−2−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−2i2i0−i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ192-20−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ722-2-20000−2−2−2−22222ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ72i−2i0−i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ202-20−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ722-2-20000−2−2−2−22222ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−2i2i0i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ212-20−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ722-2-20000−2−2−2−22222−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ72i−2i0−i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ222-20−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ722-2-20000−2−2−2−22222−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−ζ−ζ7−2i2i0i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ234444444441-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-20000000000000
χ24444444444-21-21-2-211-2-211-2-211-2-211-2-211-2-211-2-2110000000000000
χ2544444-4-4-4-41-21-211-2-211-2-211-2-2-1-122-1-122-1-122-1-1220000000000000
χ2644444-4-4-4-4-21-21-2-211-2-211-2-21122-1-122-1-122-1-122-1-10000000000000
χ27444-4-400001-21-211-2-2-1-122-1-1223i−3i003i−3i003i−3i003i−3i000000000000000
χ28444-4-400001-21-211-2-2-1-122-1-122−3i3i00−3i3i00−3i3i00−3i3i000000000000000
χ29444-4-40000-21-21-2-21122-1-122-1-1003i−3i003i−3i003i−3i003i−3i0000000000000
χ30444-4-40000-21-21-2-21122-1-122-1-100−3i3i00−3i3i00−3i3i00−3i3i0000000000000
χ3144-4002222−22−221-21-2-1-1223i−3i003i−3i002ζ2+ζ6−ζ2−2ζ6−2−22ζ2+ζ6−ζ2−2ζ6−2−2−2ζ2−ζ6ζ2+2ζ622−2ζ2−ζ6ζ2+2ζ6220000000000000
χ3244-4002222−22−221-21-2-1-122−3i3i00−3i3i00−ζ2−2ζ62ζ2+ζ6−2−2−ζ2−2ζ62ζ2+ζ6−2−2ζ2+2ζ6−2ζ2−ζ622ζ2+2ζ6−2ζ2−ζ6220000000000000
χ3344-4002222−22−22-21-2122-1-1003i−3i003i−3i−2−22ζ2+ζ6−ζ2−2ζ6−2−22ζ2+ζ6−ζ2−2ζ622−2ζ2−ζ6ζ2+2ζ622−2ζ2−ζ6ζ2+2ζ60000000000000
χ3444-4002222−22−22-21-2122-1-100−3i3i00−3i3i−2−2−ζ2−2ζ62ζ2+ζ6−2−2−ζ2−2ζ62ζ2+ζ622ζ2+2ζ6−2ζ2−ζ622ζ2+2ζ6−2ζ2−ζ60000000000000
χ3544-400−22−2222221-21-2-1-1223i−3i003i−3i00−2ζ2−ζ6ζ2+2ζ622−2ζ2−ζ6ζ2+2ζ6222ζ2+ζ6−ζ2−2ζ6−2−22ζ2+ζ6−ζ2−2ζ6−2−20000000000000
χ3644-400−22−2222221-21-2-1-122−3i3i00−3i3i00ζ2+2ζ6−2ζ2−ζ622ζ2+2ζ6−2ζ2−ζ622−ζ2−2ζ62ζ2+ζ6−2−2−ζ2−2ζ62ζ2+ζ6−2−20000000000000
χ3744-400−22−222222-21-2122-1-1003i−3i003i−3i22−2ζ2−ζ6ζ2+2ζ622−2ζ2−ζ6ζ2+2ζ6−2−22ζ2+ζ6−ζ2−2ζ6−2−22ζ2+ζ6−ζ2−2ζ60000000000000
χ3844-400−22−222222-21-2122-1-100−3i3i00−3i3i22ζ2+2ζ6−2ζ2−ζ622ζ2+2ζ6−2ζ2−ζ6−2−2−ζ2−2ζ62ζ2+ζ6−2−2−ζ2−2ζ62ζ2+ζ60000000000000
χ394-4022−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ51-2-123i−3i002ζ2+ζ6−ζ2−2ζ6−2−2−2ζ2−ζ6ζ2+2ζ6222ζ−ζ7−ζ+2ζ7−ζ−ζ7−ζ−ζ7−2ζ+ζ7ζ−2ζ7ζ+ζ7ζ+ζ7−ζ3+2ζ52ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3−2ζ5−2ζ3+ζ5ζ3+ζ5ζ3+ζ50000000000000
χ404-4022−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ51-2-12−3i3i00−ζ2−2ζ62ζ2+ζ6−2−2ζ2+2ζ6−2ζ2−ζ622−ζ+2ζ72ζ−ζ7−ζ−ζ7−ζ−ζ7ζ−2ζ7−2ζ+ζ7ζ+ζ7ζ+ζ72ζ3−ζ5−ζ3+2ζ5−ζ3−ζ5−ζ3−ζ5−2ζ3+ζ5ζ3−2ζ5ζ3+ζ5ζ3+ζ50000000000000
χ414-4022−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5-212-1003i−3i−2−22ζ2+ζ6−ζ2−2ζ622−2ζ2−ζ6ζ2+2ζ6−ζ−ζ7−ζ−ζ72ζ−ζ7−ζ+2ζ7ζ+ζ7ζ+ζ7−2ζ+ζ7ζ−2ζ7−ζ3−ζ5−ζ3−ζ5−ζ3+2ζ52ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3−2ζ5−2ζ3+ζ50000000000000
χ424-4022−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5-212-100−3i3i−2−2−ζ2−2ζ62ζ2+ζ622ζ2+2ζ6−2ζ2−ζ6−ζ−ζ7−ζ−ζ7−ζ+2ζ72ζ−ζ7ζ+ζ7ζ+ζ7ζ−2ζ7−2ζ+ζ7−ζ3−ζ5−ζ3−ζ52ζ3−ζ5−ζ3+2ζ5ζ3+ζ5ζ3+ζ5−2ζ3+ζ5ζ3−2ζ50000000000000
χ434-4022−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ51-2-123i−3i002ζ2+ζ6−ζ2−2ζ6−2−2−2ζ2−ζ6ζ2+2ζ622−2ζ+ζ7ζ−2ζ7ζ+ζ7ζ+ζ72ζ−ζ7−ζ+2ζ7−ζ−ζ7−ζ−ζ7ζ3−2ζ5−2ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3+2ζ52ζ3−ζ5−ζ3−ζ5−ζ3−ζ50000000000000
χ444-4022−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ51-2-12−3i3i00−ζ2−2ζ62ζ2+ζ6−2−2ζ2+2ζ6−2ζ2−ζ622ζ−2ζ7−2ζ+ζ7ζ+ζ7ζ+ζ7−ζ+2ζ72ζ−ζ7−ζ−ζ7−ζ−ζ7−2ζ3+ζ5ζ3−2ζ5ζ3+ζ5ζ3+ζ52ζ3−ζ5−ζ3+2ζ5−ζ3−ζ5−ζ3−ζ50000000000000
χ454-4022−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5-212-1003i−3i−2−22ζ2+ζ6−ζ2−2ζ622−2ζ2−ζ6ζ2+2ζ6ζ+ζ7ζ+ζ7−2ζ+ζ7ζ−2ζ7−ζ−ζ7−ζ−ζ72ζ−ζ7−ζ+2ζ7ζ3+ζ5ζ3+ζ5ζ3−2ζ5−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3+2ζ52ζ3−ζ50000000000000
χ464-4022−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5-212-100−3i3i−2−2−ζ2−2ζ62ζ2+ζ622ζ2+2ζ6−2ζ2−ζ6ζ+ζ7ζ+ζ7ζ−2ζ7−2ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ+2ζ72ζ−ζ7ζ3+ζ5ζ3+ζ5−2ζ3+ζ5ζ3−2ζ5−ζ3−ζ5−ζ3−ζ52ζ3−ζ5−ζ3+2ζ50000000000000
χ474-40−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ71-2-123i−3i00−2ζ2−ζ6ζ2+2ζ6222ζ2+ζ6−ζ2−2ζ6−2−2−ζ3+2ζ52ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3−2ζ5−2ζ3+ζ5ζ3+ζ5ζ3+ζ5−2ζ+ζ7ζ−2ζ7ζ+ζ7ζ+ζ72ζ−ζ7−ζ+2ζ7−ζ−ζ7−ζ−ζ70000000000000
χ484-40−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ71-2-12−3i3i00ζ2+2ζ6−2ζ2−ζ622−ζ2−2ζ62ζ2+ζ6−2−22ζ3−ζ5−ζ3+2ζ5−ζ3−ζ5−ζ3−ζ5−2ζ3+ζ5ζ3−2ζ5ζ3+ζ5ζ3+ζ5ζ−2ζ7−2ζ+ζ7ζ+ζ7ζ+ζ7−ζ+2ζ72ζ−ζ7−ζ−ζ7−ζ−ζ70000000000000
χ494-40−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7-212-1003i−3i22−2ζ2−ζ6ζ2+2ζ6−2−22ζ2+ζ6−ζ2−2ζ6−ζ3−ζ5−ζ3−ζ5−ζ3+2ζ52ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3−2ζ5−2ζ3+ζ5ζ+ζ7ζ+ζ7−2ζ+ζ7ζ−2ζ7−ζ−ζ7−ζ−ζ72ζ−ζ7−ζ+2ζ70000000000000
χ504-40−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7-212-100−3i3i22ζ2+2ζ6−2ζ2−ζ6−2−2−ζ2−2ζ62ζ2+ζ6−ζ3−ζ5−ζ3−ζ52ζ3−ζ5−ζ3+2ζ5ζ3+ζ5ζ3+ζ5−2ζ3+ζ5ζ3−2ζ5ζ+ζ7ζ+ζ7ζ−2ζ7−2ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ+2ζ72ζ−ζ70000000000000
χ514-40−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ71-2-123i−3i00−2ζ2−ζ6ζ2+2ζ6222ζ2+ζ6−ζ2−2ζ6−2−2ζ3−2ζ5−2ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3+2ζ52ζ3−ζ5−ζ3−ζ5−ζ3−ζ52ζ−ζ7−ζ+2ζ7−ζ−ζ7−ζ−ζ7−2ζ+ζ7ζ−2ζ7ζ+ζ7ζ+ζ70000000000000
χ524-40−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ71-2-12−3i3i00ζ2+2ζ6−2ζ2−ζ622−ζ2−2ζ62ζ2+ζ6−2−2−2ζ3+ζ5ζ3−2ζ5ζ3+ζ5ζ3+ζ52ζ3−ζ5−ζ3+2ζ5−ζ3−ζ5−ζ3−ζ5−ζ+2ζ72ζ−ζ7−ζ−ζ7−ζ−ζ7ζ−2ζ7−2ζ+ζ7ζ+ζ7ζ+ζ70000000000000
χ534-40−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7-212-1003i−3i22−2ζ2−ζ6ζ2+2ζ6−2−22ζ2+ζ6−ζ2−2ζ6ζ3+ζ5ζ3+ζ5ζ3−2ζ5−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3+2ζ52ζ3−ζ5−ζ−ζ7−ζ−ζ72ζ−ζ7−ζ+2ζ7ζ+ζ7ζ+ζ7−2ζ+ζ7ζ−2ζ70000000000000
χ544-40−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7-212-100−3i3i22ζ2+2ζ6−2ζ2−ζ6−2−2−ζ2−2ζ62ζ2+ζ6ζ3+ζ5ζ3+ζ5−2ζ3+ζ5ζ3−2ζ5−ζ3−ζ5−ζ3−ζ52ζ3−ζ5−ζ3+2ζ5−ζ−ζ7−ζ−ζ7−ζ+2ζ72ζ−ζ7ζ+ζ7ζ+ζ7ζ−2ζ7−2ζ+ζ70000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.