Finite Group Databasebeta

← Group #6871

Character table — Group #6871

Order 243.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size111111111333333333333333333333333999999999999999999
order133333333333333999999999999999999999999999999999999
χ1111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ3111111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ5111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ6111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ7111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ8111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ9111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ101−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ81−1+i32−1−i32ζζ4ζ71−1+i32−1−i32ζ2ζ5ζ8ζ2ζ5ζ8ζζ4ζ7
χ111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8−1+i32−1−i321ζ4ζ7ζ−1−i321−1+i32ζ8ζ2ζ5ζ5ζ8ζ2ζ7ζζ4
χ121−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8−1−i321−1+i32ζ7ζζ4−1+i32−1−i321ζ5ζ8ζ2ζ8ζ2ζ5ζ4ζ7ζ
χ131−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ51−1+i32−1−i32ζ4ζ7ζ1−1+i32−1−i32ζ8ζ2ζ5ζ8ζ2ζ5ζ4ζ7ζ
χ141−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5−1+i32−1−i321ζ7ζζ4−1−i321−1+i32ζ5ζ8ζ2ζ2ζ5ζ8ζζ4ζ7
χ151−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5−1−i321−1+i32ζζ4ζ7−1+i32−1−i321ζ2ζ5ζ8ζ5ζ8ζ2ζ7ζζ4
χ161−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ21−1+i32−1−i32ζ7ζζ41−1+i32−1−i32ζ5ζ8ζ2ζ5ζ8ζ2ζ7ζζ4
χ171−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2−1+i32−1−i321ζζ4ζ7−1−i321−1+i32ζ2ζ5ζ8ζ8ζ2ζ5ζ4ζ7ζ
χ181−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2−1−i321−1+i32ζ4ζ7ζ−1+i32−1−i321ζ8ζ2ζ5ζ2ζ5ζ8ζζ4ζ7
χ191−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ71−1−i32−1+i32ζ2ζ8ζ51−1−i32−1+i32ζ4ζζ7ζ4ζζ7ζ2ζ8ζ5
χ201−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7−1+i321−1−i32ζ5ζ2ζ8−1−i32−1+i321ζζ7ζ4ζ7ζ4ζζ8ζ5ζ2
χ211−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7−1−i32−1+i321ζ8ζ5ζ2−1+i321−1−i32ζ7ζ4ζζζ7ζ4ζ5ζ2ζ8
χ221−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ41−1−i32−1+i32ζ5ζ2ζ81−1−i32−1+i32ζζ7ζ4ζζ7ζ4ζ5ζ2ζ8
χ231−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4−1+i321−1−i32ζ8ζ5ζ2−1−i32−1+i321ζ7ζ4ζζ4ζζ7ζ2ζ8ζ5
χ241−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4−1−i32−1+i321ζ2ζ8ζ5−1+i321−1−i32ζ4ζζ7ζ7ζ4ζζ8ζ5ζ2
χ251−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζ1−1−i32−1+i32ζ8ζ5ζ21−1−i32−1+i32ζ7ζ4ζζ7ζ4ζζ8ζ5ζ2
χ261−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζ−1+i321−1−i32ζ2ζ8ζ5−1−i32−1+i321ζ4ζζ7ζζ7ζ4ζ5ζ2ζ8
χ271−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζ−1−i32−1+i321ζ5ζ2ζ8−1+i321−1−i32ζζ7ζ4ζ4ζζ7ζ2ζ8ζ5
χ28333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000
χ29333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000
χ30333−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i320000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4000000000000000000
χ31333−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4000000000000000000
χ32333−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4000000000000000000
χ33333−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32000000ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5000000000000000000
χ34333−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32000000ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5000000000000000000
χ35333−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32000000−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5000000000000000000
χ363−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i3233−3+3i32000000000000000000000000000000000000
χ373−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i323−3−3i32−3+3i323000000000000000000000000000000000000
χ383−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32330000003+i32−3+i32−i3−3+i32−i33+i32−i33+i32−3+i323−i32−3−i32i3i33−i32−3−i32−3−i32i33−i32000000000000000000
χ393−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i3233000000−3+i32−i33+i32−i33+i32−3+i323+i32−3+i32−i3−3−i32i33−i323−i32−3−i32i3i33−i32−3−i32000000000000000000
χ403−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i3233000000−i33+i32−3+i323+i32−3+i32−i3−3+i32−i33+i32i33−i32−3−i32−3−i32i33−i323−i32−3−i32i3000000000000000000
χ413−3+3i32−3−3i32−3−3i32−3+3i3233−3−3i32−3+3i32000000ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ52ζ+ζ4−ζ+ζ4−ζ−2ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4000000000000000000
χ423−3+3i32−3−3i32−3−3i32−3+3i3233−3−3i32−3+3i32000000ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5−ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ4000000000000000000
χ433−3+3i32−3−3i32−3−3i32−3+3i3233−3−3i32−3+3i32000000−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5−ζ−2ζ42ζ+ζ4−ζ+ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4000000000000000000
χ443−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i323−3+3i32−3−3i323000000000000000000000000000000000000
χ453−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i3233−3−3i32000000000000000000000000000000000000
χ463−3−3i32−3+3i32−3+3i32−3−3i3233−3+3i32−3−3i320000002ζ+ζ4−ζ+ζ4−ζ−2ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ4ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5000000000000000000
χ473−3−3i32−3+3i32−3+3i32−3−3i3233−3+3i32−3−3i32000000−ζ+ζ4−ζ−2ζ42ζ+ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ4−ζ−2ζ42ζ+ζ4−ζ+ζ4−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5000000000000000000
χ483−3−3i32−3+3i32−3+3i32−3−3i3233−3+3i32−3−3i32000000−ζ−2ζ42ζ+ζ4−ζ+ζ4−ζ+ζ4−ζ−2ζ42ζ+ζ42ζ+ζ4−ζ+ζ4−ζ−2ζ4ζ2+2ζ5ζ2−ζ5−2ζ2−ζ5ζ2−ζ5−2ζ2−ζ5ζ2+2ζ5−2ζ2−ζ5ζ2+2ζ5ζ2−ζ5000000000000000000
χ493−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233000000i33−i32−3−i323−i32−3−i32i3−3−i32i33−i32−i33+i32−3+i32−3+i32−i33+i323+i32−3+i32−i3000000000000000000
χ503−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32330000003−i32−3−i32i3−3−i32i33−i32i33−i32−3−i323+i32−3+i32−i3−i33+i32−3+i32−3+i32−i33+i32000000000000000000
χ513−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233000000−3−i32i33−i32i33−i32−3−i323−i32−3−i32i3−3+i32−i33+i323+i32−3+i32−i3−i33+i32−3+i32000000000000000000

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