Finite Group Databasebeta

← Group #13164656

Character table — Group #13164656

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111111333333666666666666161616161616161616161616222222666666121212121212121212121212323232323232323232323232333333999999181818181818181818181818484848484848484848484848
order1233662266664444121212121212121299999918181818181836336666666612121212121212121212121299999918181818181822666622666644441212121212121212181818181818181818181818
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ3111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ411−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ811−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ811−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ8
χ511−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ511−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ511−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ5
χ611−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ2
χ711−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ711−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ711−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ7
χ811−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ411−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ411−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ4
χ911−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ11−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ11−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ
χ102-222-2-22-22-22-2000000000000-1-1-1-1-1-11111112-222-2-22-22-22-2000000000000-1-1-1-1-1-11111112-222-2-22-22-22-2000000000000-1-1-1-1-1-1111111
χ112-222-2-22-22-22-20000000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i322-222-2-22-22-22-20000000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i322-222-2-22-22-22-20000000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ122-222-2-22-22-22-20000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i322-222-2-22-22-22-20000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i322-222-2-22-22-22-20000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ132-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ−ζ4−ζ7−ζ2−ζ5−ζ8ζζ4ζ7ζ2ζ5ζ82-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ−ζ4−ζ7−ζ2−ζ5−ζ8ζζ4ζ7ζ2ζ5ζ82-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ−ζ4−ζ7−ζ2−ζ5−ζ8ζζ4ζ7ζ2ζ5ζ8
χ142-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ4−ζ7−ζ−ζ8−ζ2−ζ5ζ4ζ7ζζ8ζ2ζ52-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ4−ζ7−ζ−ζ8−ζ2−ζ5ζ4ζ7ζζ8ζ2ζ52-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ4−ζ7−ζ−ζ8−ζ2−ζ5ζ4ζ7ζζ8ζ2ζ5
χ152-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ7−ζ−ζ4−ζ5−ζ8−ζ2ζ7ζζ4ζ5ζ8ζ22-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ7−ζ−ζ4−ζ5−ζ8−ζ2ζ7ζζ4ζ5ζ8ζ22-2−1+i3−1−i31−i31+i32-2−1+i31−i3−1−i31+i3000000000000−ζ7−ζ−ζ4−ζ5−ζ8−ζ2ζ7ζζ4ζ5ζ8ζ2
χ162-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ2−ζ8−ζ5−ζ4−ζ−ζ7ζ2ζ8ζ5ζ4ζζ72-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ2−ζ8−ζ5−ζ4−ζ−ζ7ζ2ζ8ζ5ζ4ζζ72-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ2−ζ8−ζ5−ζ4−ζ−ζ7ζ2ζ8ζ5ζ4ζζ7
χ172-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ5−ζ2−ζ8−ζ−ζ7−ζ4ζ5ζ2ζ8ζζ7ζ42-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ5−ζ2−ζ8−ζ−ζ7−ζ4ζ5ζ2ζ8ζζ7ζ42-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ5−ζ2−ζ8−ζ−ζ7−ζ4ζ5ζ2ζ8ζζ7ζ4
χ182-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ8−ζ5−ζ2−ζ7−ζ4−ζζ8ζ5ζ2ζ7ζ4ζ2-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ8−ζ5−ζ2−ζ7−ζ4−ζζ8ζ5ζ2ζ7ζ4ζ2-2−1−i3−1+i31+i31−i32-2−1−i31+i3−1+i31−i3000000000000−ζ8−ζ5−ζ2−ζ7−ζ4−ζζ8ζ5ζ2ζ7ζ4ζ
χ19333333333333-1-1-1-1-1-1-1-1-1-1-1-1000000000000333333333333-1-1-1-1-1-1-1-1-1-1-1-1000000000000333333333333-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ20333333-1-1-1-1-1-13-1-1-13-1-1-13-1-1-1000000000000333333-1-1-1-1-1-13-1-1-13-1-1-13-1-1-1000000000000333333-1-1-1-1-1-13-1-1-13-1-1-13-1-1-1000000000000
χ21333333-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1000000000000333333-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1000000000000333333-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1000000000000
χ22333333-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1000000000000333333-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1000000000000333333-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1000000000000
χ23333333-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13000000000000333333-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13000000000000333333-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13000000000000
χ2433−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ2533−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i323-1-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i323-1-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i323-1-1-1−3+3i321−i321−i321−i32−3−3i321+i321+i321+i32000000000000
χ2633−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-13-1-11−i32−3+3i321−i321−i321+i32−3−3i321+i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-13-1-11−i32−3+3i321−i321−i321+i32−3−3i321+i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-13-1-11−i32−3+3i321−i321−i321+i32−3−3i321+i321+i32000000000000
χ2733−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-13-11−i321−i32−3+3i321−i321+i321+i32−3−3i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-13-11−i321−i32−3+3i321−i321+i321+i32−3−3i321+i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-13-11−i321−i32−3+3i321−i321+i321+i32−3−3i321+i32000000000000
χ2833−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-1-131−i321−i321−i32−3+3i321+i321+i321+i32−3−3i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-1-131−i321−i321−i32−3+3i321+i321+i321+i32−3−3i3200000000000033−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-1-131−i321−i321−i32−3+3i321+i321+i321+i32−3−3i32000000000000
χ2933−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ3033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i323-1-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i323-1-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i323-1-1-1−3−3i321+i321+i321+i32−3+3i321−i321−i321−i32000000000000
χ3133−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-13-1-11+i32−3−3i321+i321+i321−i32−3+3i321−i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-13-1-11+i32−3−3i321+i321+i321−i32−3+3i321−i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-13-1-11+i32−3−3i321+i321+i321−i32−3+3i321−i321−i32000000000000
χ3233−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-13-11+i321+i32−3−3i321+i321−i321−i32−3+3i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-13-11+i321+i32−3−3i321+i321−i321−i32−3+3i321−i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-13-11+i321+i32−3−3i321+i321−i321−i32−3+3i321−i32000000000000
χ3333−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-1-131+i321+i321+i32−3−3i321−i321−i321−i32−3+3i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-1-131+i321+i321+i32−3−3i321−i321−i321−i32−3+3i3200000000000033−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-1-131+i321+i321+i32−3−3i321−i321−i321−i32−3+3i32000000000000
χ346-666-6-6-22-22-220000000000000000000000006-666-6-6-22-22-220000000000000000000000006-666-6-6-22-22-22000000000000000000000000
χ356-6−3+3i3−3−3i33−3i33+3i3-221−i3−1+i31+i3−1−i30000000000000000000000006-6−3+3i3−3−3i33−3i33+3i3-221−i3−1+i31+i3−1−i30000000000000000000000006-6−3+3i3−3−3i33−3i33+3i3-221−i3−1+i31+i3−1−i3000000000000000000000000
χ366-6−3−3i3−3+3i33+3i33−3i3-221+i3−1−i31−i3−1+i30000000000000000000000006-6−3−3i3−3+3i33+3i33−3i3-221+i3−1−i31−i3−1+i30000000000000000000000006-6−3−3i3−3+3i33+3i33−3i3-221+i3−1−i31−i3−1+i3000000000000000000000000
χ37111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ38111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32
χ39111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.