Finite Group Databasebeta

← Group #6868

Character table — Group #6868

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+i32−1−i32−1−i32−1−i32111−1+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−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32
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+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111
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−i32−1+i32−1+i32−1+i32111−1−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−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111
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+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32
χ101−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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−i32ζζ4ζ7ζζ4ζ7ζζ4ζ7ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8
χ111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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−i32ζ4ζ7ζζ4ζ7ζζ4ζ7ζζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5
χ121−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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−i32ζ7ζζ4ζ7ζζ4ζ7ζζ4ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2
χ131−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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+i32ζζ4ζ7ζ4ζ7ζζ7ζζ4ζ2ζ5ζ8ζ5ζ8ζ2ζ8ζ2ζ5
χ141−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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+i32ζ4ζ7ζζ7ζζ4ζζ4ζ7ζ8ζ2ζ5ζ2ζ5ζ8ζ5ζ8ζ2
χ151−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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+i32ζ7ζζ4ζζ4ζ7ζ4ζ7ζζ5ζ8ζ2ζ8ζ2ζ5ζ2ζ5ζ8
χ161−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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−i32111ζζ4ζ7ζ7ζζ4ζ4ζ7ζζ2ζ5ζ8ζ8ζ2ζ5ζ5ζ8ζ2
χ171−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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−i32111ζ4ζ7ζζζ4ζ7ζ7ζζ4ζ8ζ2ζ5ζ5ζ8ζ2ζ2ζ5ζ8
χ181−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i3211−1+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−i32111ζ7ζζ4ζ4ζ7ζζζ4ζ7ζ5ζ8ζ2ζ2ζ5ζ8ζ8ζ2ζ5
χ191−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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+i32ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ4ζζ7ζ4ζζ7ζ4ζζ7
χ201−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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+i32ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζζ7ζ4ζζ7ζ4ζζ7ζ4
χ211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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+i32ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ7ζ4ζζ7ζ4ζζ7ζ4ζ
χ221−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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+i32111ζ2ζ8ζ5ζ5ζ2ζ8ζ8ζ5ζ2ζ4ζζ7ζ7ζ4ζζζ7ζ4
χ231−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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+i32111ζ5ζ2ζ8ζ8ζ5ζ2ζ2ζ8ζ5ζζ7ζ4ζ4ζζ7ζ7ζ4ζ
χ241−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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+i32111ζ8ζ5ζ2ζ2ζ8ζ5ζ5ζ2ζ8ζ7ζ4ζζζ7ζ4ζ4ζζ7
χ251−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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−i32ζ2ζ8ζ5ζ8ζ5ζ2ζ5ζ2ζ8ζ4ζζ7ζζ7ζ4ζ7ζ4ζ
χ261−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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−i32ζ5ζ2ζ8ζ2ζ8ζ5ζ8ζ5ζ2ζζ7ζ4ζ7ζ4ζζ4ζζ7
χ271−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i3211−1−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−i32ζ8ζ5ζ2ζ5ζ2ζ8ζ2ζ8ζ5ζ7ζ4ζζ4ζζ7ζζ7ζ4
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
χ3033−3+3i323−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32000000ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5000000000000000000
χ3133−3+3i323−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32000000ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5000000000000000000
χ3233−3+3i323−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32000000−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5000000000000000000
χ3333−3−3i323−3+3i32−3−3i32−3+3i32−3+3i32−3−3i320000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4000000000000000000
χ3433−3−3i323−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4000000000000000000
χ3533−3−3i323−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4000000000000000000
χ363−3+3i323−3−3i323−3−3i32−3+3i32−3−3i32−3+3i320000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4000000000000000000
χ373−3+3i323−3−3i323−3−3i32−3+3i32−3−3i32−3+3i32000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4000000000000000000
χ383−3+3i323−3−3i323−3−3i32−3+3i32−3−3i32−3+3i32000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4000000000000000000
χ393−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3−3i3233−3+3i32000000000000000000000000000000000000
χ403−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3−3i32−3+3i323−3−3i32−3+3i323000000000000000000000000000000000000
χ413−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32−3−3i3233000000ζ+2ζ4ζ−ζ4−2ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5000000000000000000
χ423−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32−3−3i3233000000ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5000000000000000000
χ433−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32−3−3i3233000000−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5000000000000000000
χ443−3−3i323−3+3i323−3+3i32−3−3i32−3+3i32−3−3i32000000ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5000000000000000000
χ453−3−3i323−3+3i323−3+3i32−3−3i32−3+3i32−3−3i32000000ζ−ζ4−2ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5000000000000000000
χ463−3−3i323−3+3i323−3+3i32−3−3i32−3+3i32−3−3i32000000−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5000000000000000000
χ473−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32330000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4000000000000000000
χ483−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32−3+3i3233000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ4ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4000000000000000000
χ493−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32−3+3i3233000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−ζ2+ζ5−ζ2−2ζ52ζ2+ζ52ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ4ζ−ζ4−2ζ−ζ4ζ+2ζ4−2ζ−ζ4ζ+2ζ4ζ−ζ4000000000000000000
χ503−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3+3i32−3−3i323−3+3i32−3−3i323000000000000000000000000000000000000
χ513−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3+3i3233−3−3i32000000000000000000000000000000000000

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