Finite Group Databasebeta

← Group #13164544

Character table — Group #13164544

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1122222222666121212121212121212121212121212121212121212323232323232323232323232323232323232108108216216216
order12369991818182224666121218181818181818181836363636363633366699999918181818181822444
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1
χ32222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000
χ42222-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000
χ52222-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1222-1-1-100000
χ62222-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-122200000
χ722-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ52222-1-1-1-1-1ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ52-1-12-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ500000
χ822-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ52222-1-1-1-1-1ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5-12-1-12-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ+ζ8ζ4+ζ5ζ+ζ8ζ2+ζ700000
χ922-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ52222-1-1-1-1-1ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5-1-12-1-12ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ+ζ8ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ+ζ800000
χ1022-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ82222-1-1-1-1-1ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ82-1-12-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ800000
χ1122-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ82222-1-1-1-1-1ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8-12-1-12-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ2+ζ7ζ+ζ8ζ2+ζ7ζ4+ζ500000
χ1222-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ82222-1-1-1-1-1ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8-1-12-1-12ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ2+ζ7ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ2+ζ700000
χ1322-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ72222-1-1-1-1-1ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ72-1-12-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ700000
χ1422-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ72222-1-1-1-1-1ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7-12-1-12-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ+ζ800000
χ1522-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ72222-1-1-1-1-1ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7-1-12-1-12ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ4+ζ500000
χ1633333333333-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-1000000000000000000111-1-1
χ1733333333333-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-1000000000000000000-1-1-111
χ183333333333-13-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-100000000000000000011-11-1
χ193333333333-13-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1000000000000000000-1-11-11
χ203333333333-1-13-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-100000000000000000011-1-11
χ213333333333-1-13-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1000000000000000000-1-111-1
χ224-44-4444-4-4-4000000000000000000000000111-1-1-1111111-1-1-1-1-1-12-2000
χ234-44-4444-4-4-4000000000000000000000000111-1-1-1111111-1-1-1-1-1-1-22000
χ246666666666-2-2-22-2-2-222-2-2-2-2-2-2-2-2-222222200000000000000000000000
χ256666-3-3-3-3-3-36-2-2-26-2-2-2-2-311-311-31111111100000000000000000000000
χ266666-3-3-3-3-3-3-26-2-2-26-2-2-21-311-311-3111111100000000000000000000000
χ276666-3-3-3-3-3-3-2-26-2-2-26-2-211-311-311-311111100000000000000000000000
χ286666-3-3-3-3-3-3-2-2-22-2-2-222111111111−1+2i3−1−2i3−1+2i3−1−2i3−1+2i3−1−2i300000000000000000000000
χ296666-3-3-3-3-3-3-2-2-22-2-2-222111111111−1−2i3−1+2i3−1−2i3−1+2i3−1−2i3−1+2i300000000000000000000000
χ3066-3-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ56-2-2-2-311113ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ500000000000000000000000
χ3166-3-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-26-2-21-3111−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ500000000000000000000000
χ3266-3-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-2-26-211-311−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ500000000000000000000000
χ3366-3-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-2-2-22111−1+2i3−1−2i3−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ53ζ−ζ8−ζ+3ζ8−ζ2+3ζ73ζ2−ζ73ζ4−ζ5−ζ4+3ζ500000000000000000000000
χ3466-3-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-2-2-22111−1−2i3−1+2i3−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ+3ζ83ζ−ζ83ζ2−ζ7−ζ2+3ζ7−ζ4+3ζ53ζ4−ζ500000000000000000000000
χ3566-3-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ86-2-2-2-311113ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ+3ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ800000000000000000000000
χ3666-3-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-26-2-21-3111−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ800000000000000000000000
χ3766-3-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-2-26-211-311−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ800000000000000000000000
χ3866-3-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-2-2-22111−1+2i3−1−2i3−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2+3ζ73ζ2−ζ73ζ4−ζ5−ζ4+3ζ53ζ−ζ8−ζ+3ζ800000000000000000000000
χ3966-3-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-2-2-22111−1−2i3−1+2i3−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ83ζ2−ζ7−ζ2+3ζ7−ζ4+3ζ53ζ4−ζ5−ζ+3ζ83ζ−ζ800000000000000000000000
χ4066-3-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ76-2-2-2-311113ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ700000000000000000000000
χ4166-3-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-26-2-21-3111−ζ4−ζ53ζ4+3ζ5−ζ4−ζ5−ζ−ζ83ζ+3ζ8−ζ−ζ8−ζ2−ζ73ζ2+3ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ700000000000000000000000
χ4266-3-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-2-26-211-311−ζ4−ζ5−ζ4−ζ53ζ4+3ζ5−ζ−ζ8−ζ−ζ83ζ+3ζ8−ζ2−ζ7−ζ2−ζ73ζ2+3ζ7−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ700000000000000000000000
χ4366-3-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-2-2-22111−1+2i3−1−2i3−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ73ζ4−ζ5−ζ4+3ζ53ζ−ζ8−ζ+3ζ8−ζ2+3ζ73ζ2−ζ700000000000000000000000
χ4466-3-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-2-2-22111−1−2i3−1+2i3−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4+3ζ53ζ4−ζ5−ζ+3ζ83ζ−ζ83ζ2−ζ7−ζ2+3ζ700000000000000000000000
χ458-88-8888-8-8-8000000000000000000000000-1-1-1111-1-1-1-1-1-111111100000
χ468-88-8-4-4-4444000000000000000000000000222-2-2-2-1-1-1-1-1-111111100000
χ478-88-8-4-4-4444000000000000000000000000-1-1-1111222-1-1-1-2-2-211100000
χ488-88-8-4-4-4444000000000000000000000000-1-1-1111-1-1-1222111-2-2-200000
χ498-8-444ζ+4ζ84ζ2+4ζ74ζ4+4ζ5−4ζ−4ζ8−4ζ2−4ζ7−4ζ4−4ζ50000000000000000000000002-1-1-211ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ500000
χ508-8-444ζ+4ζ84ζ2+4ζ74ζ4+4ζ5−4ζ−4ζ8−4ζ2−4ζ7−4ζ4−4ζ5000000000000000000000000-12-11-21ζ2+ζ7ζ4+ζ5ζ+ζ8ζ4+ζ5ζ+ζ8ζ2+ζ7−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ4−ζ5−ζ−ζ8−ζ2−ζ700000
χ518-8-444ζ+4ζ84ζ2+4ζ74ζ4+4ζ5−4ζ−4ζ8−4ζ2−4ζ7−4ζ4−4ζ5000000000000000000000000-1-1211-2ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ+ζ8−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ−ζ800000
χ528-8-444ζ2+4ζ74ζ4+4ζ54ζ+4ζ8−4ζ2−4ζ7−4ζ4−4ζ5−4ζ−4ζ80000000000000000000000002-1-1-211ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ800000
χ538-8-444ζ2+4ζ74ζ4+4ζ54ζ+4ζ8−4ζ2−4ζ7−4ζ4−4ζ5−4ζ−4ζ8000000000000000000000000-12-11-21ζ4+ζ5ζ+ζ8ζ2+ζ7ζ+ζ8ζ2+ζ7ζ4+ζ5−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ−ζ8−ζ2−ζ7−ζ4−ζ500000
χ548-8-444ζ2+4ζ74ζ4+4ζ54ζ+4ζ8−4ζ2−4ζ7−4ζ4−4ζ5−4ζ−4ζ8000000000000000000000000-1-1211-2ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ+ζ8ζ2+ζ7−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ2−ζ700000
χ558-8-444ζ4+4ζ54ζ+4ζ84ζ2+4ζ7−4ζ4−4ζ5−4ζ−4ζ8−4ζ2−4ζ70000000000000000000000002-1-1-211ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ700000
χ568-8-444ζ4+4ζ54ζ+4ζ84ζ2+4ζ7−4ζ4−4ζ5−4ζ−4ζ8−4ζ2−4ζ7000000000000000000000000-12-11-21ζ+ζ8ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ+ζ8−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ2−ζ7−ζ4−ζ5−ζ−ζ800000
χ578-8-444ζ4+4ζ54ζ+4ζ84ζ2+4ζ7−4ζ4−4ζ5−4ζ−4ζ8−4ζ2−4ζ7000000000000000000000000-1-1211-2ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ2+ζ7ζ4+ζ5−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ4−ζ500000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.