Finite Group Databasebeta

← Group #11757416

Character table — Group #11757416

Order 972.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111111333333333333333999999999999999999999999999999121212121212121212121212121212121212363636363636363636363636
order133333333233333366666666666666999999181818181818181818181818181818181818333333333333333333999999999999
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ3111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ5111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ6111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ7111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ8111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ9111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ10111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ8
χ11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32ζ4ζ7ζζ5ζ8ζ2ζ7ζζ4ζ8ζ2ζ5
χ12111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζζ4ζ7ζ2ζ5ζ8ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111ζ7ζζ4ζ8ζ2ζ5ζ4ζ7ζζ5ζ8ζ2
χ13111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ5
χ14111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32ζ7ζζ4ζ2ζ5ζ8ζζ4ζ7ζ5ζ8ζ2
χ15111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ4ζ7ζζ8ζ2ζ5ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111ζζ4ζ7ζ5ζ8ζ2ζ7ζζ4ζ2ζ5ζ8
χ16111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ2
χ17111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32ζζ4ζ7ζ8ζ2ζ5ζ4ζ7ζζ2ζ5ζ8
χ18111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ7ζζ4ζ5ζ8ζ2ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111ζ4ζ7ζζ2ζ5ζ8ζζ4ζ7ζ8ζ2ζ5
χ19111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ7
χ20111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111ζ5ζ2ζ8ζ7ζ4ζζ8ζ5ζ2ζζ7ζ4
χ21111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ2ζ8ζ5ζ4ζζ7ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32ζ8ζ5ζ2ζζ7ζ4ζ5ζ2ζ8ζ7ζ4ζ
χ22111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ4
χ23111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111ζ8ζ5ζ2ζ4ζζ7ζ2ζ8ζ5ζ7ζ4ζ
χ24111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ5ζ2ζ8ζζ7ζ4ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32ζ2ζ8ζ5ζ7ζ4ζζ8ζ5ζ2ζ4ζζ7
χ25111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζ111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ
χ26111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζ−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111ζ2ζ8ζ5ζζ7ζ4ζ5ζ2ζ8ζ4ζζ7
χ27111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ8ζ5ζ2ζ7ζ4ζζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζ−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32ζ5ζ2ζ8ζ4ζζ7ζ2ζ8ζ5ζζ7ζ4
χ283333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000000000000000000000
χ293333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000000000000000000000
χ30333333333-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ31333333333-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000000000000000000000000000
χ32333333333-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000000000000000000000000000
χ33333333333-1−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i320000002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000000000
χ34333333333-1−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i32000000−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3000000000000000000000000000000
χ35333333333-1−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i32000000−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32000000000000000000000000000000
χ36333333333-1−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i320000002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000000000
χ37333333333-1−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i32000000−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32000000000000000000000000000000
χ38333333333-1−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i32000000−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3000000000000000000000000000000
χ39333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i32−3−3i3233−3+3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32−3−3i3233−3+3i32000000000000000000000000000000000000000000000000000000
χ40333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323−3−3i32−3+3i323−3−3i32−3+3i32333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i323−3−3i32−3+3i323000000000000000000000000000000000000000000000000000000
χ41333−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-133−3+3i32−3+3i32−3−3i32−3−3i32-1-11−i321+i321−i321−i321+i321+i32-1-11−i321−i321+i321+i323ζ3ζ43ζ73ζ23ζ53ζ8−ζ−ζ−ζ−ζ4−ζ4−ζ4−ζ7−ζ7−ζ7−ζ2−ζ2−ζ2−ζ5−ζ5−ζ5−ζ8−ζ8−ζ8000000000000000000000000000000
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χ849−9−9i32−9+9i32−9−9i32−9+9i32−9+9i3299−9−9i32-30000003+3i323−3i323+3i323−3i323−3i32-3-33+3i32000000000000000000000000000000000000000000000000000000000000

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