Finite Group Databasebeta

← Group #13049241

Character table — Group #13049241

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11133333333999999999999912121212121212121212121216161616161636363636363636363636363648484848484848484848
order1332233666626666666666669999999999999999991818181818181818181818183333339999
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+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
χ3111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−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
χ4111111111111111111111111−1+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−i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32
χ5111111111111111111111111−1+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+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1−i32−1−i32−1+i32−1+i32
χ6111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−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−i321111
χ7111111111111111111111111−1−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+i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32
χ8111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+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+i321111
χ9111111111111111111111111−1−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−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1+i32−1+i32−1−i32−1−i32
χ1011111−1+i32−1−i321111111−1+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+i32−1−i321−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ1111111−1+i32−1−i321111111−1+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−i321−1−i321−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1−i3211−1+i32
χ1211111−1+i32−1−i321111111−1+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−i321−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1+i32−1−i321−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i3211−1+i32−1−i321
χ1311111−1+i32−1−i321111111−1+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+i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i321−1+i32−1−i321−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i3211−1+i32
χ1411111−1+i32−1−i321111111−1+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−i321−1+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−i321−1+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321
χ1511111−1+i32−1−i321111111−1+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−i321−1+i32−1+i32−1−i321111111−1+i32−1−i321−1−i321−1+i32−1−i321−1+i32−1+i32−1−i321−1+i32−1−i321−1−i321−1+i32−1+i32−1−i32−1+i32−1−i32
χ1611111−1+i32−1−i321111111−1+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−i321−1+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−i321−1+i32−1−i32−1+i32−1−i321−1−i321−1+i321−1+i32−1−i321
χ1711111−1+i32−1−i321111111−1+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+i32−1−i321−1−i321−1+i32111111−1−i321−1+i32−1+i32−1−i321−1+i32−1−i321−1−i321−1+i32−1−i321−1+i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ1811111−1+i32−1−i321111111−1+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+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1−i3211−1+i32
χ1911111−1−i32−1+i321111111−1−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−i32−1+i321−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ2011111−1−i32−1+i321111111−1−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+i321−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1−i32−1+i321−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i3211−1−i32−1+i321
χ2111111−1−i32−1+i321111111−1−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+i321−1+i321−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1+i3211−1−i32
χ2211111−1−i32−1+i321111111−1−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+i321−1−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+i321−1−i32−1+i32−1−i32−1+i321−1+i321−1−i321−1−i32−1+i321
χ2311111−1−i32−1+i321111111−1−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−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1+i3211−1−i32
χ2411111−1−i32−1+i321111111−1−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−i32−1+i321−1+i321−1−i32111111−1+i321−1−i32−1−i32−1+i321−1−i32−1+i321−1+i321−1−i32−1+i321−1−i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ2511111−1−i32−1+i321111111−1−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−i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i321−1−i32−1+i321−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i3211−1−i32
χ2611111−1−i32−1+i321111111−1−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+i321−1−i32−1−i32−1+i321111111−1−i32−1+i321−1+i321−1−i32−1+i321−1−i32−1−i32−1+i321−1−i32−1+i321−1+i321−1−i32−1−i32−1+i32−1−i32−1+i32
χ2711111−1−i32−1+i321111111−1−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+i321−1−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+i321−1−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321
χ283333-13333-1-1-1-1-13-1-1-1-13-1-1-1-1000000333333000000000000-1-1-1-1-1-10000000000
χ293333-13333-1-1-1-1-13-1-1-1-13-1-1-1-1000000−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i320000000000001−i321−i321−i321+i321+i321+i320000000000
χ303333-13333-1-1-1-1-13-1-1-1-13-1-1-1-1000000−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i320000000000001+i321+i321+i321−i321−i321−i320000000000
χ313333-1−3+3i32−3−3i3233-1-1-1-1-1−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i320000003−3+3i32−3−3i323−3+3i32−3−3i32000000000000-11−i321+i32-11−i321+i320000000000
χ323333-1−3+3i32−3−3i3233-1-1-1-1-1−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i32000000−3+3i32−3−3i323−3−3i323−3+3i320000000000001−i321+i32-11+i32-11−i320000000000
χ333333-1−3+3i32−3−3i3233-1-1-1-1-1−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i32000000−3−3i323−3+3i32−3+3i32−3−3i3230000000000001+i32-11−i321−i321+i32-10000000000
χ343333-1−3−3i32−3+3i3233-1-1-1-1-1−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i320000003−3−3i32−3+3i323−3−3i32−3+3i32000000000000-11+i321−i32-11+i321−i320000000000
χ353333-1−3−3i32−3+3i3233-1-1-1-1-1−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i32000000−3+3i323−3−3i32−3−3i32−3+3i3230000000000001−i32-11+i321+i321−i32-10000000000
χ363333-1−3−3i32−3+3i3233-1-1-1-1-1−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i32000000−3−3i32−3+3i323−3+3i323−3−3i320000000000001+i321−i32-11−i32-11+i320000000000
χ37333-1333-1-133-1-1-1-13-1-1-1-13-1-1-1333333000000000000-1-1-1-1-1-10000000000000000
χ38333-1333-1-133-1-1-1-13-1-1-1-13-1-1-1−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i320000000000001−i321−i321−i321+i321+i321+i320000000000000000
χ39333-1333-1-133-1-1-1-13-1-1-1-13-1-1-1−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i320000000000001+i321+i321+i321−i321−i321−i320000000000000000
χ40333-13−3+3i32−3−3i32-1-133-1-1-11−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i323−3+3i32−3−3i323−3+3i32−3−3i32000000000000-11−i321+i32-11−i321+i320000000000000000
χ41333-13−3+3i32−3−3i32-1-133-1-1-11−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i32−3+3i32−3−3i323−3−3i323−3+3i320000000000001−i321+i32-11+i32-11−i320000000000000000
χ42333-13−3+3i32−3−3i32-1-133-1-1-11−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i32−3−3i323−3+3i32−3+3i32−3−3i3230000000000001+i32-11−i321−i321+i32-10000000000000000
χ43333-13−3−3i32−3+3i32-1-133-1-1-11+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i323−3−3i32−3+3i323−3−3i32−3+3i32000000000000-11+i321−i32-11+i321−i320000000000000000
χ44333-13−3−3i32−3+3i32-1-133-1-1-11+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i32−3+3i323−3−3i32−3−3i32−3+3i3230000000000001−i32-11+i321+i321−i32-10000000000000000
χ45333-13−3−3i32−3+3i32-1-133-1-1-11+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i32−3−3i32−3+3i323−3+3i323−3−3i320000000000001+i321−i32-11−i32-11+i320000000000000000
χ463−3+3i32−3−3i323300−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3200000000000000000000003ζ23ζ53ζ83ζ3ζ43ζ70000000000000000000000
χ473−3+3i32−3−3i323300−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3200000000000000000000003ζ53ζ83ζ23ζ73ζ3ζ40000000000000000000000
χ483−3+3i32−3−3i323300−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3200000000000000000000003ζ83ζ23ζ53ζ43ζ73ζ0000000000000000000000
χ493−3−3i32−3+3i323300−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3200000000000000000000003ζ3ζ73ζ43ζ53ζ23ζ80000000000000000000000
χ503−3−3i32−3+3i323300−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3200000000000000000000003ζ43ζ3ζ73ζ23ζ83ζ50000000000000000000000
χ513−3−3i32−3+3i323300−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3200000000000000000000003ζ73ζ43ζ3ζ83ζ53ζ20000000000000000000000
χ52999-3-399-3-3-3-3111-3-3111-3-31110000000000000000000000000000000000000000
χ53999-3-3−9+9i32−9−9i32-3-3-3-31113−3i323−3i32−1+i32−1+i32−1+i323+3i323+3i32−1−i32−1−i32−1−i320000000000000000000000000000000000000000
χ54999-3-3−9−9i32−9+9i32-3-3-3-31113+3i323+3i32−1−i32−1−i32−1−i323−3i323−3i32−1+i32−1+i32−1+i320000000000000000000000000000000000000000
χ559−9+9i32−9−9i329-300−9+9i32−9−9i323−3i323+3i32-33−3i323+3i3200000000000000000000000000000000000000000000000000
χ569−9+9i32−9−9i32-39003−3i323+3i32−9+9i32−9−9i32-33−3i323+3i3200000000000000000000000000000000000000000000000000
χ579−9+9i32−9−9i32-3-3003−3i323+3i323−3i323+3i321−1+i32−1−i32004−2+2i3−2−2i3004−2+2i3−2−2i30000000000000000000000000000000000000000
χ589−9+9i32−9−9i32-3-3003−3i323+3i323−3i323+3i321−1+i32−1−i3200−2+2i3−2−2i3400−2−2i34−2+2i30000000000000000000000000000000000000000
χ599−9+9i32−9−9i32-3-3003−3i323+3i323−3i323+3i321−1+i32−1−i3200−2−2i34−2+2i300−2+2i3−2−2i340000000000000000000000000000000000000000
χ609−9−9i32−9+9i329-300−9−9i32−9+9i323+3i323−3i32-33+3i323−3i3200000000000000000000000000000000000000000000000000
χ619−9−9i32−9+9i32-39003+3i323−3i32−9−9i32−9+9i32-33+3i323−3i3200000000000000000000000000000000000000000000000000
χ629−9−9i32−9+9i32-3-3003+3i323−3i323+3i323−3i321−1−i32−1+i32004−2−2i3−2+2i3004−2−2i3−2+2i30000000000000000000000000000000000000000
χ639−9−9i32−9+9i32-3-3003+3i323−3i323+3i323−3i321−1−i32−1+i3200−2+2i34−2−2i300−2−2i3−2+2i340000000000000000000000000000000000000000
χ649−9−9i32−9+9i32-3-3003+3i323−3i323+3i323−3i321−1−i32−1+i3200−2−2i3−2+2i3400−2+2i34−2−2i30000000000000000000000000000000000000000

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