Finite Group Databasebeta

← Group #13049229

Character table — Group #13049229

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11133333333999999999999912121212121212121212121216161616161636363636363636363636363648484848484848484848
order1332266669926618181818181818181818333399999999999999666618181818181818183333999999
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i321111−1+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
χ311111111111111111111111111−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i321111−1−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−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+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−i32−1−i3211−1+i32−1−i321111−1+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+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321
χ7111111111111111111111111−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−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−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321
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+i32−1+i3211−1−i32−1+i321111−1−i32
χ10111111111−1+i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+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−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ11111111111−1+i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i321−1−i3211−1+i321
χ12111111111−1+i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211−1−i32−1+i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1−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−i32
χ13111111111−1+i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i3211−1−i3211−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i3211−1−i3211−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i3211
χ14111111111−1+i32−1−i32111−1+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−i3211−1+i32−1−i3211−1+i32111111−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32
χ15111111111−1+i32−1−i32111−1+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−i3211−1+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−i3211−1+i321−1+i32−1−i3211−1+i32−1−i321−1−i32−1−i3211−1+i32−1+i32
χ16111111111−1+i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32111111−1−i32−1+i32111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i3211−1+i32−1−i32
χ17111111111−1+i32−1−i32111−1+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−i3211−1+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−i3211−1+i321−1−i32−1+i321−1−i321−1+i32−1−i321−1+i32
χ18111111111−1+i32−1−i32111−1+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−i3211−1+i32−1−i321−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i32−1−i3211−1+i32−1−i321−1+i3211−1−i321−1+i32−1−i32−1+i32−1−i321
χ19111111111−1−i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−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+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ20111111111−1−i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211−1+i32−1−i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1+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+i32
χ21111111111−1−i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i321−1+i3211−1−i321
χ22111111111−1−i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32111111−1+i32−1−i32111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i3211−1−i32−1+i32
χ23111111111−1−i32−1+i32111−1−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+i3211−1−i32−1+i321−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i32−1+i3211−1−i32−1+i321−1−i3211−1+i321−1−i32−1+i32−1−i32−1+i321
χ24111111111−1−i32−1+i32111−1−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+i3211−1−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+i3211−1−i321−1+i32−1−i321−1+i321−1−i32−1+i321−1−i32
χ25111111111−1−i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i3211−1+i3211−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i3211−1+i3211−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i3211
χ26111111111−1−i32−1+i32111−1−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+i3211−1−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+i3211−1−i321−1−i32−1+i3211−1−i32−1+i321−1+i32−1+i3211−1−i32−1−i32
χ27111111111−1−i32−1+i32111−1−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+i3211−1−i32−1+i3211−1−i32111111−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32
χ283333-133-1-133-1-1-13-1-1-1-13-1-1-1-100330000333300000000-1-10000-1-1-1-10000000000
χ293333-133-1-133-1-1-13-1-1-1-13-1-1-1-100−3+3i32−3−3i320000−3+3i32−3+3i32−3−3i32−3−3i32000000001−i321+i3200001−i321−i321+i321+i320000000000
χ303333-133-1-133-1-1-13-1-1-1-13-1-1-1-100−3−3i32−3+3i320000−3−3i32−3−3i32−3+3i32−3+3i32000000001+i321−i3200001+i321+i321−i321−i320000000000
χ313333-133-1-1−3+3i32−3−3i32-1-1-1−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i3200330000−3+3i32−3−3i32−3+3i32−3−3i3200000000-1-100001−i321+i321−i321+i320000000000
χ323333-133-1-1−3+3i32−3−3i32-1-1-1−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i3200−3+3i32−3−3i320000−3−3i3233−3+3i32000000001−i321+i3200001+i32-1-11−i320000000000
χ333333-133-1-1−3+3i32−3−3i32-1-1-1−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i3200−3−3i32−3+3i3200003−3+3i32−3−3i323000000001+i321−i320000-11−i321+i32-10000000000
χ343333-133-1-1−3−3i32−3+3i32-1-1-1−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i3200330000−3−3i32−3+3i32−3−3i32−3+3i3200000000-1-100001+i321−i321+i321−i320000000000
χ353333-133-1-1−3−3i32−3+3i32-1-1-1−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i3200−3+3i32−3−3i3200003−3−3i32−3+3i323000000001−i321+i320000-11+i321−i32-10000000000
χ363333-133-1-1−3−3i32−3+3i32-1-1-1−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i3200−3−3i32−3+3i320000−3+3i3233−3−3i32000000001+i321−i3200001−i32-1-11+i320000000000
χ37333-13-1-13333-1-1-1-13-1-1-1-13-1-1-1330033330000000000-1-100-1-1-1-100000000000000
χ38333-13-1-13333-1-1-1-13-1-1-1-13-1-1-1−3+3i32−3−3i3200−3+3i32−3+3i32−3−3i32−3−3i3200000000001−i321+i32001−i321−i321+i321+i3200000000000000
χ39333-13-1-13333-1-1-1-13-1-1-1-13-1-1-1−3−3i32−3+3i3200−3−3i32−3−3i32−3+3i32−3+3i3200000000001+i321−i32001+i321+i321−i321−i3200000000000000
χ40333-13-1-133−3+3i32−3−3i32-1-1-11−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i323300−3+3i32−3−3i32−3+3i32−3−3i320000000000-1-1001−i321+i321−i321+i3200000000000000
χ41333-13-1-133−3+3i32−3−3i32-1-1-11−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i32−3+3i32−3−3i3200−3−3i3233−3+3i3200000000001−i321+i32001+i32-1-11−i3200000000000000
χ42333-13-1-133−3+3i32−3−3i32-1-1-11−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i32−3−3i32−3+3i32003−3+3i32−3−3i32300000000001+i321−i3200-11−i321+i32-100000000000000
χ43333-13-1-133−3−3i32−3+3i32-1-1-11+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i323300−3−3i32−3+3i32−3−3i32−3+3i320000000000-1-1001+i321−i321+i321−i3200000000000000
χ44333-13-1-133−3−3i32−3+3i32-1-1-11+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i32−3+3i32−3−3i32003−3−3i32−3+3i32300000000001−i321+i3200-11+i321−i32-100000000000000
χ45333-13-1-133−3−3i32−3+3i32-1-1-11+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i32−3−3i32−3+3i3200−3+3i3233−3−3i3200000000001+i321−i32001−i32-1-11+i3200000000000000
χ463−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32003−3+3i32−3−3i3200000000000000000000003ζ3ζ43ζ73ζ23ζ53ζ80000000000000000000000
χ473−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32003−3+3i32−3−3i3200000000000000000000003ζ43ζ73ζ3ζ83ζ23ζ50000000000000000000000
χ483−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32003−3+3i32−3−3i3200000000000000000000003ζ73ζ3ζ43ζ53ζ83ζ20000000000000000000000
χ493−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32003−3−3i32−3+3i3200000000000000000000003ζ23ζ83ζ53ζ43ζ3ζ70000000000000000000000
χ503−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32003−3−3i32−3+3i3200000000000000000000003ζ53ζ23ζ83ζ3ζ73ζ40000000000000000000000
χ513−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32003−3−3i32−3+3i3200000000000000000000003ζ83ζ53ζ23ζ73ζ43ζ0000000000000000000000
χ52999-3-3-3-3-3-399111-3-3111-3-31110000000000000000000000000000000000000000
χ53999-3-3-3-3-3-3−9+9i32−9−9i321113−3i323−3i32−1+i32−1+i32−1+i323+3i323+3i32−1−i32−1−i32−1−i320000000000000000000000000000000000000000
χ54999-3-3-3-3-3-3−9−9i32−9+9i321113+3i323+3i32−1−i32−1−i32−1−i323−3i323−3i32−1+i32−1+i32−1+i320000000000000000000000000000000000000000
χ559−9+9i32−9−9i329-3−9+9i32−9−9i323−3i323+3i3200-33−3i323+3i3200000000000000000000000000000000000000000000000000
χ569−9+9i32−9−9i32-393−3i323+3i32−9+9i32−9−9i3200-33−3i323+3i3200000000000000000000000000000000000000000000000000
χ579−9+9i32−9−9i32-3-33−3i323+3i323−3i323+3i32001−1+i32−1−i32004ζ4ζ44ζ7004ζ24ζ54ζ80000000000000000000000000000000000000000
χ589−9+9i32−9−9i32-3-33−3i323+3i323−3i323+3i32001−1+i32−1−i32004ζ44ζ74ζ004ζ84ζ24ζ50000000000000000000000000000000000000000
χ599−9+9i32−9−9i32-3-33−3i323+3i323−3i323+3i32001−1+i32−1−i32004ζ74ζ4ζ4004ζ54ζ84ζ20000000000000000000000000000000000000000
χ609−9−9i32−9+9i329-3−9−9i32−9+9i323+3i323−3i3200-33+3i323−3i3200000000000000000000000000000000000000000000000000
χ619−9−9i32−9+9i32-393+3i323−3i32−9−9i32−9+9i3200-33+3i323−3i3200000000000000000000000000000000000000000000000000
χ629−9−9i32−9+9i32-3-33+3i323−3i323+3i323−3i32001−1−i32−1+i32004ζ24ζ84ζ5004ζ44ζ4ζ70000000000000000000000000000000000000000
χ639−9−9i32−9+9i32-3-33+3i323−3i323+3i323−3i32001−1−i32−1+i32004ζ54ζ24ζ8004ζ4ζ74ζ40000000000000000000000000000000000000000
χ649−9−9i32−9+9i32-3-33+3i323−3i323+3i323−3i32001−1−i32−1+i32004ζ84ζ54ζ2004ζ74ζ44ζ0000000000000000000000000000000000000000

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