Finite Group Databasebeta

← Group #11757811

Character table — Group #11757811

Order 972.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size11133333999999999999999912121212121227272727272736363636363636363636363636363636
order1332336666999999991818181818189999991818181818183333333399999999
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ3111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ4111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i321−1−i32−1−i32−1−i321−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32
χ5111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111−1−i32111
χ6111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111−1+i32111−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ7111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i321−1+i32−1+i32−1+i321−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32
χ8111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111−1−i32111−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ9111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111−1+i32111
χ101111111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111−1+i32−1−i321−1+i32−1−i32−1+i321−1+i32−1−i32−1−i321−1+i32−1−i32−1−i321−1+i32−1−i32−1+i321−1+i32−1−i32
χ111111111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i321−1+i32−1−i3211−1−i321−1+i32
χ121111111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1+i32−1−i321−1+i32−1−i321−1−i321−1+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321
χ131111111111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i321
χ141111111111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32
χ151111111111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i32
χ161111111111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1−i321−1+i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32
χ171111111111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1−i32−1+i321−1+i32−1−i321−1−i321−1+i321−1+i32−1−i321
χ181111111111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i321−1+i32−1+i32−1−i3211−1+i32−1−i3211−1−i321−1+i32−1+i321−1+i32−1−i32−1−i321−1+i32−1−i32
χ191111111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111−1−i32−1+i321−1−i32−1+i32−1−i321−1−i32−1+i32−1+i321−1−i32−1+i32−1+i321−1−i32−1+i32−1−i321−1−i32−1+i32
χ201111111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1−i32−1+i321−1−i32−1+i321−1+i321−1−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321
χ211111111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i321−1−i32−1+i3211−1+i321−1−i32
χ221111111111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1+i321−1−i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32
χ231111111111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i321−1−i32−1−i32−1+i3211−1−i32−1+i3211−1+i321−1−i32−1−i321−1−i32−1+i32−1+i321−1−i32−1+i32
χ241111111111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1+i32−1−i321−1−i32−1+i321−1+i321−1−i321−1−i32−1+i321
χ251111111111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i321
χ261111111111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i32
χ271111111111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32
χ283333−3+3i32−3−3i3233−3+3i32−3−3i32000000000000003−3+3i32−3−3i323−3+3i32−3−3i320000000000000000000000
χ293333−3+3i32−3−3i3233−3+3i32−3−3i3200000000000000−3+3i32−3−3i323−3−3i323−3+3i320000000000000000000000
χ303333−3+3i32−3−3i3233−3+3i32−3−3i3200000000000000−3−3i323−3+3i32−3+3i32−3−3i3230000000000000000000000
χ313333−3−3i32−3+3i3233−3−3i32−3+3i32000000000000003−3−3i32−3+3i323−3−3i32−3+3i320000000000000000000000
χ323333−3−3i32−3+3i3233−3−3i32−3+3i3200000000000000−3+3i323−3−3i32−3−3i32−3+3i3230000000000000000000000
χ333333−3−3i32−3+3i3233−3−3i32−3+3i3200000000000000−3−3i32−3+3i323−3+3i323−3−3i320000000000000000000000
χ34333-133-1-1-1-133333333-1-1-1-1-1-1000000-1-1-1-1-1-10000000000000000
χ35333-133-1-1-1-133−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-1-1-10000001−i321−i321−i321+i321+i321+i320000000000000000
χ36333-133-1-1-1-133−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-1-1-10000001+i321+i321+i321−i321−i321−i320000000000000000
χ37333-133-1-1-1-1−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i321−i321−i321−i321+i321+i321+i32000000-11−i321+i32-11−i321+i320000000000000000
χ38333-133-1-1-1-1−3+3i32−3−3i32−3+3i32−3−3i323−3−3i323−3+3i321−i321−i321−i321+i321+i321+i320000001−i321+i32-11+i32-11−i320000000000000000
χ39333-133-1-1-1-1−3+3i32−3−3i32−3−3i323−3+3i32−3+3i32−3−3i3231−i321−i321−i321+i321+i321+i320000001+i32-11−i321−i321+i32-10000000000000000
χ40333-133-1-1-1-1−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i321+i321+i321+i321−i321−i321−i32000000-11+i321−i32-11+i321−i320000000000000000
χ41333-133-1-1-1-1−3−3i32−3+3i32−3+3i323−3−3i32−3−3i32−3+3i3231+i321+i321+i321−i321−i321−i320000001−i32-11+i321+i321−i32-10000000000000000
χ42333-133-1-1-1-1−3−3i32−3+3i32−3−3i32−3+3i323−3+3i323−3−3i321+i321+i321+i321−i321−i321−i320000001+i321−i32-11−i32-11+i320000000000000000
χ43999-3−9+9i32−9−9i32-3-33−3i323+3i32000000000000000000000000000000000000000000
χ44999-3−9−9i32−9+9i32-3-33+3i323−3i32000000000000000000000000000000000000000000
χ459−9+9i32−9−9i32900−9+9i32−9−9i3200000000000000000000000000000000000000000000
χ469−9+9i32−9−9i32-3003−3i323+3i3200000000002ζ+4ζ42ζ−2ζ4−4ζ−2ζ44ζ2+2ζ5−2ζ2+2ζ5−2ζ2−4ζ50000000000000000000000000000
χ479−9+9i32−9−9i32-3003−3i323+3i3200000000002ζ−2ζ4−4ζ−2ζ42ζ+4ζ4−2ζ2+2ζ5−2ζ2−4ζ54ζ2+2ζ50000000000000000000000000000
χ489−9+9i32−9−9i32-3003−3i323+3i320000000000−4ζ−2ζ42ζ+4ζ42ζ−2ζ4−2ζ2−4ζ54ζ2+2ζ5−2ζ2+2ζ50000000000000000000000000000
χ499−9−9i32−9+9i32900−9−9i32−9+9i3200000000000000000000000000000000000000000000
χ509−9−9i32−9+9i32-3003+3i323−3i3200000000004ζ2+2ζ5−2ζ2+2ζ5−2ζ2−4ζ52ζ−2ζ4−4ζ−2ζ42ζ+4ζ40000000000000000000000000000
χ519−9−9i32−9+9i32-3003+3i323−3i320000000000−2ζ2+2ζ5−2ζ2−4ζ54ζ2+2ζ5−4ζ−2ζ42ζ+4ζ42ζ−2ζ40000000000000000000000000000
χ529−9−9i32−9+9i32-3003+3i323−3i320000000000−2ζ2−4ζ54ζ2+2ζ5−2ζ2+2ζ52ζ+4ζ42ζ−2ζ4−4ζ−2ζ40000000000000000000000000000

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