Finite Group Databasebeta

← Group #10590930

Character table — Group #10590930

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11222222222222222224444444444444444444444444441212121212121212121212122424242424247272
order1223344666688121224242424366668121212121212122424242424242424242424242424246688121224242424441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111-1-111-1-1-1-111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-111-1-11-1
χ611111111111-1-111-1-1-1-111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-11
χ711111111111-1-111-1-1-1-111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-1-11
χ811111111111-1-111-1-1-1-111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-1111-1
χ922222-2-2222200-2-20000222220-2-2-2-2-2-2-20000000000000000002i−2i002i2i−2i−2i00000000
χ1022222-2-2222200-2-20000222220-2-2-2-2-2-2-2000000000000000000−2i2i00−2i−2i2i2i00000000
χ112222-12222-1222-1-1-1-1-1-1-1-1-1-1-12-12-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000
χ122222-12222-1222-1-1-1-1-1-1-1-1-1-1-12-12-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-2-211-2-211111100000000
χ132222-12222-12-2-2-1-11111-1-1-1-1-1-2-12-1-12-1-111-2-2-2-21111111122-1-1-2-2-1-1111100000000
χ142222-12222-12-2-2-1-11111-1-1-1-1-1-2-12-1-12-1-111-2-2-2-211111111-2-2112211-1-1-1-100000000
χ152222-1-2-222-12001133−3−3-1-1-1-1-101-211-2113−300003333−3−3−3−300−i3i32i−2i−i3i3−i−iii00000000
χ162222-1-2-222-12001133−3−3-1-1-1-1-101-211-2113−300003333−3−3−3−300i3−i3−2i2ii3−i3ii−i−i00000000
χ172222-1-2-222-120011−3−333-1-1-1-1-101-211-211−330000−3−3−3−3333300−i3i3−2i2i−i3i3ii−i−i00000000
χ182222-1-2-222-120011−3−333-1-1-1-1-101-211-211−330000−3−3−3−3333300i3−i32i−2ii3−i3−i−iii00000000
χ19222-1222-1-12-122222222-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100
χ20222-1222-1-12-122222222-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2111100
χ21222-1222-1-12-1-2-222-2-2-2-2-12-1-1-1-22-1-1-1-1-1-1-2-21111111111110000000000002-2-1-11100
χ22222-1222-1-12-1-2-222-2-2-2-2-12-1-1-1-22-1-1-1-1-1-1-2-2111111111111000000000000-2211-1-100
χ2322-2222-2-2-222222222222-2-2-22-2-2-2-2-2222-2-222-2-222-2-222-2-200000000000000000000
χ2422-2222-2-2-222-2-222-2-2-2-22-2-2-222-2-2-2-222222-2-222-2-222-2-22200000000000000000000
χ2522-222-22-2-22200-2-200002-2-2-2202222-2-2-2000000000000002-22200-2-2000000000000
χ2622-222-22-2-22200-2-200002-2-2-2202222-2-2-200000000000000-22-2-20022000000000000
χ2722-22-12-2-2-2-1222-1-1-1-1-1-1-1111-1-21-2112-1-11122-2-2-1-111-1-11100−i3i300i3−i3−i3i3−i3i300000000
χ2822-22-12-2-2-2-1222-1-1-1-1-1-1-1111-1-21-2112-1-11122-2-2-1-111-1-11100i3−i300−i3i3i3−i3i3−i300000000
χ2922-22-12-2-2-2-12-2-2-1-11111-1111-121-2112-1-1-1-1-2-22211-1-111-1-100−i3i300i3−i3i3−i3i3−i300000000
χ3022-22-12-2-2-2-12-2-2-1-11111-1111-121-2112-1-1-1-1-2-22211-1-111-1-100i3−i300−i3i3−i3i3−i3i300000000
χ3122-22-1-22-2-2-12001133−3−3-1111-10-12-1-1-211−33000033−3−3−3−3332-2-1-100113−3−3300000000
χ3222-22-1-22-2-2-12001133−3−3-1111-10-12-1-1-211−33000033−3−3−3−333-221100-1-1−333−300000000
χ3322-22-1-22-2-2-120011−3−333-1111-10-12-1-1-2113−30000−3−33333−3−32-2-1-10011−333−300000000
χ3422-22-1-22-2-2-120011−3−333-1111-10-12-1-1-2113−30000−3−33333−3−3-221100-1-13−3−3300000000
χ3522-2-122-2112-122222222-1-211-1-2-2111-1-1-1-2-2-1-111-1-111-1-11100000000000000−i3i3−i3i300
χ3622-2-122-2112-122222222-1-211-1-2-2111-1-1-1-2-2-1-111-1-111-1-11100000000000000i3−i3i3−i300
χ3722-2-122-2112-1-2-222-2-2-2-2-1-211-12-2111-1-1-12211-1-111-1-111-1-100000000000000−i3i3i3−i300
χ3822-2-122-2112-1-2-222-2-2-2-2-1-211-12-2111-1-1-12211-1-111-1-111-1-100000000000000i3−i3−i3i300
χ39444-24-4-4-2-24-200-4-40000-24-2-2-20-42222220000000000000000000000000000000000
χ40444-2-244-2-2-2-244-2-2-2-2-2-21-21114-2-211-211-2-2-2-2-2-21111111100000000000000000000
χ41444-2-244-2-2-2-2-4-4-2-222221-2111-4-2-211-211222222-1-1-1-1-1-1-1-100000000000000000000
χ42444-2-2-4-4-2-2-2-200222323−23−231-2111022-1-12-1-123−230000−3−3−3−3333300000000000000000000
χ43444-2-2-4-4-2-2-2-20022−23−2323231-2111022-1-12-1-1−232300003333−3−3−3−300000000000000000000
χ4444-4-24-44224-200-4-40000-2-422-204-2-2-22220000000000000000000000000000000000
χ4544-4-2-24-422-2-244-2-2-2-2-2-212-1-11-422-1-1-21122-2-22211-1-111-1-100000000000000000000
χ4644-4-2-24-422-2-2-4-4-2-2222212-1-11422-1-1-211-2-222-2-2-1-111-1-11100000000000000000000
χ4744-4-2-2-4422-2-200222323−23−2312-1-110-2-2112-1-1−23230000−3−33333−3−300000000000000000000
χ4844-4-2-2-4422-2-20022−23−23232312-1-110-2-2112-1-123−23000033−3−3−3−33300000000000000000000
χ494-40440000-4-422−220022−2222−224000-4000000000022−220022−220022−220000000000000000000000
χ504-40440000-4-4−222200−2222−22224000-40000000000−222200−222200−22220000000000000000000000
χ514-404-200002-422−2223−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23-2000200000023−230022−22002ζ5−2ζ7−2ζ5+2ζ7002ζ13−2ζ23−2ζ13+2ζ230000000000000000000000
χ524-404-200002-422−22−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7-20002000000−23230022−22002ζ13−2ζ23−2ζ13+2ζ23002ζ5−2ζ7−2ζ5+2ζ70000000000000000000000
χ534-404-200002-4−222223−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23-2000200000023−2300−222200−2ζ5+2ζ72ζ5−2ζ700−2ζ13+2ζ232ζ13−2ζ230000000000000000000000
χ544-404-200002-4−2222−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7-20002000000−232300−222200−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ70000000000000000000000
χ554-40-2400−2i32i3-4222−220022−2222−22-20−2i32i320000000000−22i6−i6−22i6−i6−22i6−i600000000000000000000
χ564-40-2400−2i32i3-42−222200−2222−2222-20−2i32i3200000000002−2−i6i62−2−i6i62−2−i6i600000000000000000000
χ574-40-24002i3−2i3-4222−220022−2222−22-202i3−2i320000000000−22−i6i6−22−i6i6−22−i6i600000000000000000000
χ584-40-24002i3−2i3-42−222200−2222−2222-202i3−2i3200000000002−2i6−i62−2i6−i62−2i6−i600000000000000000000
χ594-40-2-200−2i32i32222−2223−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310i3−i3-10003i−3i0−3300−22i6−i6−ζ5+ζ7ζ5−ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ13+ζ23ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000
χ604-40-2-200−2i32i32222−22−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ710i3−i3-1000−3i3i03−300−22i6−i6−ζ13+ζ23ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000
χ614-40-2-200−2i32i322−222223−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310i3−i3-10003i−3i0−33002−2−i6i6ζ5−ζ7−ζ5+ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ13−ζ23−ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000
χ624-40-2-200−2i32i322−2222−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710i3−i3-1000−3i3i03−3002−2−i6i6ζ13−ζ23−ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000
χ634-40-2-2002i3−2i32222−2223−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310−i3i3-1000−3i3i0−3300−22−i6i6−ζ5+ζ7ζ5−ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ13+ζ23ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000
χ644-40-2-2002i3−2i32222−22−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ710−i3i3-10003i−3i03−300−22−i6i6−ζ13+ζ23ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000
χ654-40-2-2002i3−2i322−222223−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310−i3i3-1000−3i3i0−33002−2i6−i6ζ5−ζ7−ζ5+ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ13−ζ23−ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000
χ664-40-2-2002i3−2i322−2222−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710−i3i3-10003i−3i03−3002−2i6−i6ζ13−ζ23−ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.