Finite Group Databasebeta

← Group #10624613

Character table — Group #10624613

Order 729.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size1111111113333333333339999999999999999999999999999999999999999272727272727272727272727
order1333333339999999999993333333399999999999999999999999999999999339999999999
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111−1+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−i3211111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ311111111111111111111111111111−1−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+i3211111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111111111111111−1+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
χ511111111111111111111111−1+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+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
χ611111111111111111111111−1+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+i32−1+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−i321111
χ711111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111111111111111−1−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
χ811111111111111111111111−1−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−i32−1−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+i321111
χ911111111111111111111111−1−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−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
χ10111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111111−1+i32−1+i32−1+i32−1−i32−1−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+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ11111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−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−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1−i3211−1+i32
χ12111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−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−i32−1+i32−1−i321−1+i32−1+i32−1−i3211−1+i32−1−i321
χ13111111111−1+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+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i3211−1+i32
χ14111111111−1+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+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1−i32−1+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321
χ15111111111−1+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+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i3211−1+i32−1−i321−1−i321−1+i32−1+i32−1−i32−1+i32−1−i32
χ16111111111−1+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−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1+i32−1+i32−1−i321−1−i321−1+i321−1+i32−1−i321
χ17111111111−1+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−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1−i321−1+i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ18111111111−1+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−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1−i3211−1+i32
χ19111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111111−1−i32−1−i32−1−i32−1+i32−1+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−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ20111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+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+i32−1−i32−1+i321−1−i32−1−i32−1+i3211−1−i32−1+i321
χ21111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+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+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1+i3211−1−i32
χ22111111111−1−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+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1−i32−1−i32−1+i321−1+i321−1−i321−1−i32−1+i321
χ23111111111−1−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+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1+i3211−1−i32
χ24111111111−1−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+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1+i321−1−i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ25111111111−1−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−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i3211−1−i32
χ26111111111−1−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−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1+i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i3211−1−i32−1+i321−1+i321−1−i32−1−i32−1+i32−1−i32−1+i32
χ27111111111−1−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−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1+i32−1−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321
χ28333333333333−3+3i32−3+3i32−3+3i32333−3−3i32−3−3i32−3−3i32−3+3i32−3−3i32000000000000000000000000−3−3i32−3+3i32000000000000000000000000
χ29333333333333−3−3i32−3−3i32−3−3i32333−3+3i32−3+3i32−3+3i32−3−3i32−3+3i32000000000000000000000000−3+3i32−3−3i32000000000000000000000000
χ30333333333−3+3i32−3+3i32−3+3i32333−3−3i32−3−3i32−3−3i32333−3−3i32−3+3i32000000000000000000000000−3−3i32−3+3i32000000000000000000000000
χ31333333333−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i3200000000000000000000000033000000000000000000000000
χ32333333333−3−3i32−3−3i32−3−3i32333−3+3i32−3+3i32−3+3i32333−3+3i32−3−3i32000000000000000000000000−3+3i32−3−3i32000000000000000000000000
χ33333333333−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i3200000000000000000000000033000000000000000000000000
χ34333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ3ζ43ζ70003ζ23ζ53ζ800000000ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5i33−i32−3−i322ζ2+ζ5−ζ2+ζ5−ζ2−2ζ53+i32−3+i32−i32ζ+ζ4−ζ+ζ4−ζ−2ζ400000000000000000000000000
χ35333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ3ζ43ζ70003ζ23ζ53ζ800000000ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ53−i32−3−i32i3−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−3+i32−i33+i32−ζ+ζ4−ζ−2ζ42ζ+ζ400000000000000000000000000
χ36333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ3ζ43ζ70003ζ23ζ53ζ800000000−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−3−i32i33−i32−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−i33+i32−3+i32−ζ−2ζ42ζ+ζ4−ζ+ζ400000000000000000000000000
χ37333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ43ζ73ζ0003ζ83ζ23ζ500000000ζ+2ζ4ζ−ζ4−2ζ−ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ53−i32−3−i32i32ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−3+i32−i33+i32−ζ−2ζ42ζ+ζ4−ζ+ζ400000000000000000000000000
χ38333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ43ζ73ζ0003ζ83ζ23ζ500000000ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−3−i32i33−i32−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−i33+i32−3+i322ζ+ζ4−ζ+ζ4−ζ−2ζ400000000000000000000000000
χ39333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ43ζ73ζ0003ζ83ζ23ζ500000000−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5i33−i32−3−i32−ζ2−2ζ52ζ2+ζ5−ζ2+ζ53+i32−3+i32−i3−ζ+ζ4−ζ−2ζ42ζ+ζ400000000000000000000000000
χ40333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ73ζ3ζ40003ζ53ζ83ζ200000000ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5−3−i32i33−i322ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−i33+i32−3+i32−ζ+ζ4−ζ−2ζ42ζ+ζ400000000000000000000000000
χ41333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i320003ζ73ζ3ζ40003ζ53ζ83ζ200000000ζ−ζ4−2ζ−ζ4ζ+2ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5i33−i32−3−i32−ζ2+ζ5−ζ2−2ζ52ζ2+ζ53+i32−3+i32−i3−ζ−2ζ42ζ+ζ4−ζ+ζ400000000000000000000000000
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.