Finite Group Databasebeta

← Group #13164554

Character table — Group #13164554

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1122222222666121212121212121212121212121212121212121212323232323232323232323232323232323232108108216216216
order12333366662442666666666666121212121212121299999999918181818181818181844288
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
χ4222-1-1-12-1-1-12222222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ500000
χ5222-1-1-12-1-1-12222222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ800000
χ6222-1-1-12-1-1-12222222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ700000
χ722-12-1-1-12-1-12222-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ500000
χ822-12-1-1-12-1-12222-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ800000
χ922-12-1-1-12-1-12222-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ700000
χ1022-1-12-1-1-12-12222-1-1-1-1-1-1222-1-1-1-1-1-1-122-1-1ζ+ζ8ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ+ζ8ζ2+ζ7ζ+ζ8ζ4+ζ5ζ+ζ8ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ+ζ8ζ2+ζ7ζ+ζ8ζ4+ζ500000
χ1122-1-12-1-1-12-12222-1-1-1-1-1-1222-1-1-1-1-1-1-122-1-1ζ2+ζ7ζ+ζ8ζ4+ζ5ζ+ζ8ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ+ζ8ζ2+ζ7ζ+ζ8ζ4+ζ5ζ+ζ8ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ+ζ800000
χ1222-1-12-1-1-12-12222-1-1-1-1-1-1222-1-1-1-1-1-1-122-1-1ζ4+ζ5ζ2+ζ7ζ+ζ8ζ2+ζ7ζ+ζ8ζ4+ζ5ζ+ζ8ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ+ζ8ζ2+ζ7ζ+ζ8ζ4+ζ5ζ+ζ8ζ4+ζ5ζ2+ζ700000
χ1322-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1200000
χ1422-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-12-1-1-122-1-1-12-1-1-122-1-100000
χ1522-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-12-1-1-122-1-1-12-100000
χ1633333333333-1-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-1000000000000000000111-1-1
χ1733333333333-1-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-1000000000000000000-1-1-111
χ183333333333-13-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-13-100000000000000000011-11-1
χ193333333333-13-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-13-1000000000000000000-1-11-11
χ203333333333-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-1300000000000000000011-1-11
χ213333333333-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-13000000000000000000-1-111-1
χ224-44444-4-4-4-4000000000000000000000000111111111-1-1-1-1-1-1-1-1-12-2000
χ234-44444-4-4-4-4000000000000000000000000111111111-1-1-1-1-1-1-1-1-1-22000
χ246666666666-2-2-22-222-222-222-222-2-2-2-2-2-2-2-200000000000000000000000
χ25666-3-3-36-3-3-36-2-2-26-2-2-311-311-311-2-211111100000000000000000000000
χ26666-3-3-36-3-3-3-26-2-2-2-2-21111111116-2-31-31-3100000000000000000000000
χ27666-3-3-36-3-3-3-2-26-2-2-2-2111111111-261-31-31-300000000000000000000000
χ28666-3-3-36-3-3-3-2-2-22-2221−1+2i3−1−2i31−1+2i3−1−2i31−1+2i3−1−2i3-2-211111100000000000000000000000
χ29666-3-3-36-3-3-3-2-2-22-2221−1−2i3−1+2i31−1−2i3−1+2i31−1−2i3−1+2i3-2-211111100000000000000000000000
χ3066-36-3-3-36-3-36-2-2-2-3116-2-2-311-31111-2-2111100000000000000000000000
χ3166-36-3-3-36-3-3-26-2-2111-2-2-2111111-316-2-31-3100000000000000000000000
χ3266-36-3-3-36-3-3-2-26-2111-2-2-21111111-3-261-31-300000000000000000000000
χ3366-36-3-3-36-3-3-2-2-221−1+2i3−1−2i3-2221−1+2i3−1−2i31−1−2i3−1+2i311-2-2111100000000000000000000000
χ3466-36-3-3-36-3-3-2-2-221−1−2i3−1+2i3-2221−1−2i3−1+2i31−1+2i3−1−2i311-2-2111100000000000000000000000
χ3566-3-36-3-3-36-36-2-2-2-311-3116-2-2-3111111-2-21100000000000000000000000
χ3666-3-36-3-3-36-3-26-2-2111111-2-2-2111-31-316-2-3100000000000000000000000
χ3766-3-36-3-3-36-3-2-26-2111111-2-2-21111-31-3-261-300000000000000000000000
χ3866-3-36-3-3-36-3-2-2-221−1+2i3−1−2i31−1−2i3−1+2i3-2221−1+2i3−1−2i31111-2-21100000000000000000000000
χ3966-3-36-3-3-36-3-2-2-221−1−2i3−1+2i31−1+2i3−1−2i3-2221−1−2i3−1+2i31111-2-21100000000000000000000000
χ4066-3-3-36-3-3-366-2-2-2-311-311-3116-2-2111111-2-200000000000000000000000
χ4166-3-3-36-3-3-36-26-2-2111111111-2-2-2-31-31-316-200000000000000000000000
χ4266-3-3-36-3-3-36-2-26-2111111111-2-2-21-31-31-3-2600000000000000000000000
χ4366-3-3-36-3-3-36-2-2-221−1+2i3−1−2i31−1+2i3−1−2i31−1−2i3−1+2i3-222111111-2-200000000000000000000000
χ4466-3-3-36-3-3-36-2-2-221−1−2i3−1+2i31−1−2i3−1+2i31−1+2i3−1−2i3-222111111-2-200000000000000000000000
χ458-88888-8-8-8-8000000000000000000000000-1-1-1-1-1-1-1-1-111111111100000
χ468-88-4-4-4-8444000000000000000000000000ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ500000
χ478-88-4-4-4-8444000000000000000000000000ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ800000
χ488-88-4-4-4-8444000000000000000000000000ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ700000
χ498-8-48-4-44-844000000000000000000000000ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ500000
χ508-8-48-4-44-844000000000000000000000000ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ800000
χ518-8-48-4-44-844000000000000000000000000ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ700000
χ528-8-4-48-444-84000000000000000000000000ζ+ζ8ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ+ζ8ζ2+ζ7ζ+ζ8ζ4+ζ5−ζ−ζ8−ζ4−ζ5−ζ2−ζ7−ζ4−ζ5−ζ2−ζ7−ζ−ζ8−ζ2−ζ7−ζ−ζ8−ζ4−ζ500000
χ538-8-4-48-444-84000000000000000000000000ζ2+ζ7ζ+ζ8ζ4+ζ5ζ+ζ8ζ4+ζ5ζ2+ζ7ζ4+ζ5ζ2+ζ7ζ+ζ8−ζ2−ζ7−ζ−ζ8−ζ4−ζ5−ζ−ζ8−ζ4−ζ5−ζ2−ζ7−ζ4−ζ5−ζ2−ζ7−ζ−ζ800000
χ548-8-4-48-444-84000000000000000000000000ζ4+ζ5ζ2+ζ7ζ+ζ8ζ2+ζ7ζ+ζ8ζ4+ζ5ζ+ζ8ζ4+ζ5ζ2+ζ7−ζ4−ζ5−ζ2−ζ7−ζ−ζ8−ζ2−ζ7−ζ−ζ8−ζ4−ζ5−ζ−ζ8−ζ4−ζ5−ζ2−ζ700000
χ558-8-4-4-48444-80000000000000000000000002-1-1-12-1-1-12-2111-2111-200000
χ568-8-4-4-48444-8000000000000000000000000-12-1-1-122-1-11-2111-2-21100000
χ578-8-4-4-48444-8000000000000000000000000-1-122-1-1-12-111-2-2111-2100000

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