Finite Group Databasebeta

← Group #10624801

Character table — Group #10624801

Order 729.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size1111111113333333333339999999999999999999999999999999999999999272727272727272727272727
order1333333333333339999993333339999999999999999999999999999999999339999999999
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ3111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ4111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32
χ5111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32
χ6111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111
χ7111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32
χ8111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111
χ9111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32
χ10111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111−1+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−i32−1−i32−1−i32111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ11111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+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−i32−1+i32−1−i321−1−i321−1+i32−1−i3211−1+i32
χ12111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1−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−i32−1+i32−1−i321−1+i32−1+i32−1−i3211−1+i32−1−i321
χ13111111111111111−1+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+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−i32111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i3211−1+i32
χ14111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−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−i32−1−i32111−1+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+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321
χ15111111111111111−1+i32−1+i32−1+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+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−i32111111−1+i32−1+i32−1+i3211−1+i32−1−i321−1−i321−1+i32−1+i32−1−i32−1+i32−1−i32
χ16111111111111111−1+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+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−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
χ17111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−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−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1−i321−1+i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ18111111111111111−1+i32−1+i32−1+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+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1−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
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χ20111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1+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+i32−1−i32−1+i321−1−i32−1−i32−1+i3211−1−i32−1+i321
χ21111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−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+i32−1−i32−1+i321−1+i321−1−i32−1+i3211−1−i32
χ22111111111111111−1−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−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+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
χ23111111111111111−1−i32−1−i32−1−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−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1+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
χ24111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+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+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1+i321−1−i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ25111111111111111−1−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−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+i32111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i3211−1−i32
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χ27111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+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+i32−1+i32111−1−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−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321
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χ51333−3−3i32−3−3i32−3+3i32−3+3i32−3−3i32−3+3i320000003ζ83ζ53ζ23ζ73ζ43ζ−i33+i32−3+i323−i32−3−i32i30000000000000000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ4000000000000
χ523−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000003ζ3ζ43ζ70003ζ23ζ53ζ80000000000000000000000000000000
χ533−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000003ζ43ζ73ζ0003ζ83ζ23ζ50000000000000000000000000000000
χ543−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i323−3+3i32−3−3i323−3+3i32−3−3i320000000000000000003ζ73ζ3ζ40003ζ53ζ83ζ20000000000000000000000000000000
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χ583−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32−3−3i323−3+3i32−3+3i32−3−3i3230000000000003−3+3i32−3−3i320000003−3+3i32−3−3i320000000000000000000000000000000000
χ593−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32−3−3i323−3+3i32−3+3i32−3−3i323000000000000−3+3i32−3−3i323000000−3−3i323−3+3i320000000000000000000000000000000000
χ603−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32−3−3i323−3+3i32−3+3i32−3−3i323000000000000−3−3i323−3+3i32000000−3+3i32−3−3i3230000000000000000000000000000000000
χ613−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000003ζ23ζ83ζ50003ζ43ζ3ζ70000000000000000000000000000000
χ623−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000003ζ53ζ23ζ80003ζ3ζ73ζ40000000000000000000000000000000
χ633−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i323−3−3i32−3+3i323−3−3i32−3+3i320000000000000000003ζ83ζ53ζ20003ζ73ζ43ζ0000000000000000000000000000000
χ643−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32−3+3i323−3−3i32−3−3i32−3+3i3230000000000003−3−3i32−3+3i320000003−3−3i32−3+3i320000000000000000000000000000000000
χ653−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32−3+3i323−3−3i32−3−3i32−3+3i323000000000000−3+3i323−3−3i32000000−3−3i32−3+3i3230000000000000000000000000000000000
χ663−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32−3+3i323−3−3i32−3−3i32−3+3i323000000000000−3−3i32−3+3i323000000−3+3i323−3−3i320000000000000000000000000000000000
χ673−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32−3−3i32−3+3i323−3+3i323−3−3i320000000000000003ζ3ζ73ζ40000000003ζ53ζ23ζ80000000000000000000000000000
χ683−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32−3−3i32−3+3i323−3+3i323−3−3i320000000000000003ζ43ζ3ζ70000000003ζ23ζ83ζ50000000000000000000000000000
χ693−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32−3−3i32−3+3i323−3+3i323−3−3i320000000000000003ζ73ζ43ζ0000000003ζ83ζ53ζ20000000000000000000000000000
χ709−9+9i32−9−9i32−9+9i32−9−9i32−9−9i32−9+9i32990000000000000000000000000000000000000000000000000000000000000000
χ719−9+9i32−9−9i32−9−9i329−9+9i329−9+9i32−9−9i320000000000000000000000000000000000000000000000000000000000000000
χ729−9−9i32−9+9i32−9+9i329−9−9i329−9−9i32−9+9i320000000000000000000000000000000000000000000000000000000000000000
χ739−9−9i32−9+9i32−9−9i32−9+9i32−9+9i32−9−9i32990000000000000000000000000000000000000000000000000000000000000000

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