Finite Group Databasebeta

← Group #13152248

Character table — Group #13152248

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11133333333333121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212192192192192192192
order13326699181818181818224446666121212121212181818181818181818181818363636363636363636363636363636363636339999
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ311111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ4111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ5111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ6111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ7111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ8111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ9111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ10333333333333333-1-1-1-133-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000
χ1133333333333333-13-1-1-1-1-133-1-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000
χ1233333333333333-1-13-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1333-1-1-1-1-1-1000000
χ1333333333333333-1-1-13-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1333-1-1-1000000
χ1433333333333333-1-1-1-13-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1333000000
χ15333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i323-1-1-1-133-1-1-1-1-1-1-1-1−3+3i32−3+3i32−3+3i321−i321−i321−i32−3−3i32−3−3i32−3−3i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000
χ16333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-13-1-1-1-1-133-1-1-1-1-1-11−i321−i321−i32−3+3i32−3+3i32−3+3i321+i321+i321+i32−3−3i32−3−3i32−3−3i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000
χ17333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-13-1-1-1-1-1-133-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i32000000
χ18333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-13-1-1-1-1-1-1-133-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i321+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i32000000
χ19333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-13-1-1-1-1-1-1-1-1331−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i321+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i32000000
χ20333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i323-1-1-1-133-1-1-1-1-1-1-1-1−3−3i32−3−3i32−3−3i321+i321+i321+i32−3+3i32−3+3i32−3+3i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000
χ21333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-13-1-1-1-1-133-1-1-1-1-1-11+i321+i321+i32−3−3i32−3−3i32−3−3i321−i321−i321−i32−3+3i32−3+3i32−3+3i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000
χ22333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-13-1-1-1-1-1-133-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i32000000
χ23333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-13-1-1-1-1-1-1-133-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i321−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i32000000
χ24333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-13-1-1-1-1-1-1-1-1331+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i32000000
χ253−3+3i32−3−3i323−3+3i32−3−3i320000000033333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000
χ263−3+3i32−3−3i323−3+3i32−3−3i32000000003-1-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321+i321−i321+i320002ζ2ζ42ζ70002ζ22ζ52ζ82ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ8000000
χ273−3+3i32−3−3i323−3+3i32−3−3i32000000003-1-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321+i321−i321+i320002ζ42ζ72ζ0002ζ82ζ22ζ52ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ82ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ5000000
χ283−3+3i32−3−3i323−3+3i32−3−3i32000000003-1-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321+i321−i321+i320002ζ72ζ2ζ40002ζ52ζ82ζ22ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ82ζ2000000
χ293−3+3i32−3−3i323−3+3i32−3−3i3200000000-13-1-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321+i321−i321+i322ζ2ζ42ζ70002ζ22ζ52ζ80002ζ2ζ42ζ72ζ42ζ72ζ2ζ72ζ2ζ42ζ22ζ52ζ82ζ82ζ22ζ52ζ52ζ82ζ2000000
χ303−3+3i32−3−3i323−3+3i32−3−3i3200000000-13-1-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321+i321−i321+i322ζ42ζ72ζ0002ζ82ζ22ζ50002ζ42ζ72ζ2ζ72ζ2ζ42ζ2ζ42ζ72ζ82ζ22ζ52ζ52ζ82ζ22ζ22ζ52ζ8000000
χ313−3+3i32−3−3i323−3+3i32−3−3i3200000000-13-1-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321+i321−i321+i322ζ72ζ2ζ40002ζ52ζ82ζ20002ζ72ζ2ζ42ζ2ζ42ζ72ζ42ζ72ζ2ζ52ζ82ζ22ζ22ζ52ζ82ζ82ζ22ζ5000000
χ323−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-13-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321+i321−i321+i322ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ80002ζ72ζ2ζ42ζ42ζ72ζ0002ζ52ζ82ζ22ζ82ζ22ζ5000000
χ333−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-13-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321+i321−i321+i322ζ42ζ72ζ2ζ42ζ72ζ2ζ82ζ22ζ52ζ82ζ22ζ50002ζ2ζ42ζ72ζ72ζ2ζ40002ζ22ζ52ζ82ζ52ζ82ζ2000000
χ343−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-13-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321+i321−i321+i322ζ72ζ2ζ42ζ72ζ2ζ42ζ52ζ82ζ22ζ52ζ82ζ20002ζ42ζ72ζ2ζ2ζ42ζ70002ζ82ζ22ζ52ζ22ζ52ζ8000000
χ353−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-13-11−i321+i321−i321+i321−i321+i32−3+3i32−3−3i321−i321+i322ζ2ζ42ζ72ζ42ζ72ζ2ζ22ζ52ζ82ζ82ζ22ζ52ζ72ζ2ζ40002ζ2ζ42ζ72ζ52ζ82ζ20002ζ22ζ52ζ8000000
χ363−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-13-11−i321+i321−i321+i321−i321+i32−3+3i32−3−3i321−i321+i322ζ42ζ72ζ2ζ72ζ2ζ42ζ82ζ22ζ52ζ52ζ82ζ22ζ2ζ42ζ70002ζ42ζ72ζ2ζ22ζ52ζ80002ζ82ζ22ζ5000000
χ373−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-13-11−i321+i321−i321+i321−i321+i32−3+3i32−3−3i321−i321+i322ζ72ζ2ζ42ζ2ζ42ζ72ζ52ζ82ζ22ζ22ζ52ζ82ζ42ζ72ζ0002ζ72ζ2ζ42ζ82ζ22ζ50002ζ52ζ82ζ2000000
χ383−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-1-131−i321+i321−i321+i321−i321+i321−i321+i32−3+3i32−3−3i322ζ2ζ42ζ72ζ72ζ2ζ42ζ22ζ52ζ82ζ52ζ82ζ22ζ42ζ72ζ2ζ2ζ42ζ70002ζ82ζ22ζ52ζ22ζ52ζ8000000000
χ393−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-1-131−i321+i321−i321+i321−i321+i321−i321+i32−3+3i32−3−3i322ζ42ζ72ζ2ζ2ζ42ζ72ζ82ζ22ζ52ζ22ζ52ζ82ζ72ζ2ζ42ζ42ζ72ζ0002ζ52ζ82ζ22ζ82ζ22ζ5000000000
χ403−3+3i32−3−3i323−3+3i32−3−3i3200000000-1-1-1-131−i321+i321−i321+i321−i321+i321−i321+i32−3+3i32−3−3i322ζ72ζ2ζ42ζ42ζ72ζ2ζ52ζ82ζ22ζ82ζ22ζ52ζ2ζ42ζ72ζ72ζ2ζ40002ζ22ζ52ζ82ζ52ζ82ζ2000000000
χ413−3−3i32−3+3i323−3−3i32−3+3i320000000033333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000
χ423−3−3i32−3+3i323−3−3i32−3+3i32000000003-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321−i321+i321−i320002ζ22ζ82ζ50002ζ42ζ2ζ72ζ22ζ82ζ52ζ22ζ82ζ52ζ22ζ82ζ52ζ42ζ2ζ72ζ42ζ2ζ72ζ42ζ2ζ7000000
χ433−3−3i32−3+3i323−3−3i32−3+3i32000000003-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321−i321+i321−i320002ζ52ζ22ζ80002ζ2ζ72ζ42ζ52ζ22ζ82ζ52ζ22ζ82ζ52ζ22ζ82ζ2ζ72ζ42ζ2ζ72ζ42ζ2ζ72ζ4000000
χ443−3−3i32−3+3i323−3−3i32−3+3i32000000003-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321−i321+i321−i320002ζ82ζ52ζ20002ζ72ζ42ζ2ζ82ζ52ζ22ζ82ζ52ζ22ζ82ζ52ζ22ζ72ζ42ζ2ζ72ζ42ζ2ζ72ζ42ζ000000
χ453−3−3i32−3+3i323−3−3i32−3+3i3200000000-13-1-1-11+i321−i32−3−3i32−3+3i321+i321−i321+i321−i321+i321−i322ζ22ζ82ζ50002ζ42ζ2ζ70002ζ22ζ82ζ52ζ82ζ52ζ22ζ52ζ22ζ82ζ42ζ2ζ72ζ72ζ42ζ2ζ2ζ72ζ4000000
χ463−3−3i32−3+3i323−3−3i32−3+3i3200000000-13-1-1-11+i321−i32−3−3i32−3+3i321+i321−i321+i321−i321+i321−i322ζ52ζ22ζ80002ζ2ζ72ζ40002ζ52ζ22ζ82ζ22ζ82ζ52ζ82ζ52ζ22ζ2ζ72ζ42ζ42ζ2ζ72ζ72ζ42ζ000000
χ473−3−3i32−3+3i323−3−3i32−3+3i3200000000-13-1-1-11+i321−i32−3−3i32−3+3i321+i321−i321+i321−i321+i321−i322ζ82ζ52ζ20002ζ72ζ42ζ0002ζ82ζ52ζ22ζ52ζ22ζ82ζ22ζ82ζ52ζ72ζ42ζ2ζ2ζ72ζ42ζ42ζ2ζ7000000
χ483−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-13-1-11+i321−i321+i321−i32−3−3i32−3+3i321+i321−i321+i321−i322ζ22ζ82ζ52ζ22ζ82ζ52ζ42ζ2ζ72ζ42ζ2ζ70002ζ52ζ22ζ82ζ82ζ52ζ20002ζ2ζ72ζ42ζ72ζ42ζ000000
χ493−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-13-1-11+i321−i321+i321−i32−3−3i32−3+3i321+i321−i321+i321−i322ζ52ζ22ζ82ζ52ζ22ζ82ζ2ζ72ζ42ζ2ζ72ζ40002ζ82ζ52ζ22ζ22ζ82ζ50002ζ72ζ42ζ2ζ42ζ2ζ7000000
χ503−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-13-1-11+i321−i321+i321−i32−3−3i32−3+3i321+i321−i321+i321−i322ζ82ζ52ζ22ζ82ζ52ζ22ζ72ζ42ζ2ζ72ζ42ζ0002ζ22ζ82ζ52ζ52ζ22ζ80002ζ42ζ2ζ72ζ2ζ72ζ4000000
χ513−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-13-11+i321−i321+i321−i321+i321−i32−3−3i32−3+3i321+i321−i322ζ22ζ82ζ52ζ82ζ52ζ22ζ42ζ2ζ72ζ72ζ42ζ2ζ52ζ22ζ80002ζ22ζ82ζ52ζ2ζ72ζ40002ζ42ζ2ζ7000000
χ523−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-13-11+i321−i321+i321−i321+i321−i32−3−3i32−3+3i321+i321−i322ζ52ζ22ζ82ζ22ζ82ζ52ζ2ζ72ζ42ζ42ζ2ζ72ζ82ζ52ζ20002ζ52ζ22ζ82ζ72ζ42ζ0002ζ2ζ72ζ4000000
χ533−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-13-11+i321−i321+i321−i321+i321−i32−3−3i32−3+3i321+i321−i322ζ82ζ52ζ22ζ52ζ22ζ82ζ72ζ42ζ2ζ2ζ72ζ42ζ22ζ82ζ50002ζ82ζ52ζ22ζ42ζ2ζ70002ζ72ζ42ζ000000
χ543−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-1-131+i321−i321+i321−i321+i321−i321+i321−i32−3−3i32−3+3i322ζ22ζ82ζ52ζ52ζ22ζ82ζ42ζ2ζ72ζ2ζ72ζ42ζ82ζ52ζ22ζ22ζ82ζ50002ζ72ζ42ζ2ζ42ζ2ζ7000000000
χ553−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-1-131+i321−i321+i321−i321+i321−i321+i321−i32−3−3i32−3+3i322ζ52ζ22ζ82ζ82ζ52ζ22ζ2ζ72ζ42ζ72ζ42ζ2ζ22ζ82ζ52ζ52ζ22ζ80002ζ42ζ2ζ72ζ2ζ72ζ4000000000
χ563−3−3i32−3+3i323−3−3i32−3+3i3200000000-1-1-1-131+i321−i321+i321−i321+i321−i321+i321−i32−3−3i32−3+3i322ζ82ζ52ζ22ζ22ζ82ζ52ζ72ζ42ζ2ζ42ζ2ζ72ζ52ζ22ζ82ζ82ζ52ζ20002ζ2ζ72ζ42ζ72ζ42ζ000000000
χ57121212-4-4-41212-4-4-4-4-4-4000000000000000000000000000000000000000000000000000
χ58121212-4-4-4−6+6i3−6−6i32−2i32−2i32−2i32+2i32+2i32+2i3000000000000000000000000000000000000000000000000000
χ59121212-4-4-4−6−6i3−6+6i32+2i32+2i32+2i32−2i32−2i32−2i3000000000000000000000000000000000000000000000000000
χ6012−6+6i3−6−6i3-42−2i32+2i3008ζ8ζ48ζ78ζ28ζ58ζ8000000000000000000000000000000000000000000000000000
χ6112−6+6i3−6−6i3-42−2i32+2i3008ζ48ζ78ζ8ζ88ζ28ζ5000000000000000000000000000000000000000000000000000
χ6212−6+6i3−6−6i3-42−2i32+2i3008ζ78ζ8ζ48ζ58ζ88ζ2000000000000000000000000000000000000000000000000000
χ6312−6−6i3−6+6i3-42+2i32−2i3008ζ28ζ88ζ58ζ48ζ8ζ7000000000000000000000000000000000000000000000000000
χ6412−6−6i3−6+6i3-42+2i32−2i3008ζ58ζ28ζ88ζ8ζ78ζ4000000000000000000000000000000000000000000000000000
χ6512−6−6i3−6+6i3-42+2i32−2i3008ζ88ζ58ζ28ζ78ζ48ζ000000000000000000000000000000000000000000000000000

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