Finite Group Databasebeta

← Group #11757835

Character table — Group #11757835

Order 972.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111333339999999999121212121212363636361113333399999999991212121212123636363611133333999999999912121212121236363636
order133233663366666666999999333333363366336666666699999933333336336633666666669999993333
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1+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−i32111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ3111111111111111111−1−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+i32111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1−i32
χ511111111−1+i32−1−i3211−1+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+i3211111111−1+i32−1−i3211−1+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+i3211111111−1+i32−1−i3211−1+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
χ611111111−1+i32−1−i3211−1+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−i32111111111−1+i32−1−i3211−1+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−i32111111111−1+i32−1−i3211−1+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
χ711111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1+i32
χ811111111−1−i32−1+i3211−1−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+i32111111111−1−i32−1+i3211−1−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+i32111111111−1−i32−1+i3211−1−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
χ911111111−1−i32−1+i3211−1−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−i3211111111−1−i32−1+i3211−1−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−i3211111111−1−i32−1+i3211−1−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
χ103333−3+3i32−3−3i323300−3+3i32−3−3i3200000000000000003333−3+3i32−3−3i323300−3+3i32−3−3i3200000000000000003333−3+3i32−3−3i323300−3+3i32−3−3i320000000000000000
χ113333−3−3i32−3+3i323300−3−3i32−3+3i3200000000000000003333−3−3i32−3+3i323300−3−3i32−3+3i3200000000000000003333−3−3i32−3+3i323300−3−3i32−3+3i320000000000000000
χ12333-133-1-133-1-1-1-1-1-1-1-10000000000333-133-1-133-1-1-1-1-1-1-1-10000000000333-133-1-133-1-1-1-1-1-1-1-10000000000
χ13333-133-1-1−3+3i32−3−3i32-1-11−i321−i321−i321+i321+i321+i320000000000333-133-1-1−3+3i32−3−3i32-1-11−i321−i321−i321+i321+i321+i320000000000333-133-1-1−3+3i32−3−3i32-1-11−i321−i321−i321+i321+i321+i320000000000
χ14333-133-1-1−3−3i32−3+3i32-1-11+i321+i321+i321−i321−i321−i320000000000333-133-1-1−3−3i32−3+3i32-1-11+i321+i321+i321−i321−i321−i320000000000333-133-1-1−3−3i32−3+3i32-1-11+i321+i321+i321−i321−i321−i320000000000
χ15333-1−3+3i32−3−3i32-1-1001−i321+i322−1+i3−1−i32−1+i3−1−i30000000000333-1−3+3i32−3−3i32-1-1001−i321+i322−1+i3−1−i32−1+i3−1−i30000000000333-1−3+3i32−3−3i32-1-1001−i321+i322−1+i3−1−i32−1+i3−1−i30000000000
χ16333-1−3+3i32−3−3i32-1-1001−i321+i32−1+i3−1−i32−1−i32−1+i30000000000333-1−3+3i32−3−3i32-1-1001−i321+i32−1+i3−1−i32−1−i32−1+i30000000000333-1−3+3i32−3−3i32-1-1001−i321+i32−1+i3−1−i32−1−i32−1+i30000000000
χ17333-1−3+3i32−3−3i32-1-1001−i321+i32−1−i32−1+i3−1+i3−1−i320000000000333-1−3+3i32−3−3i32-1-1001−i321+i32−1−i32−1+i3−1+i3−1−i320000000000333-1−3+3i32−3−3i32-1-1001−i321+i32−1−i32−1+i3−1+i3−1−i320000000000
χ18333-1−3−3i32−3+3i32-1-1001+i321−i322−1−i3−1+i32−1−i3−1+i30000000000333-1−3−3i32−3+3i32-1-1001+i321−i322−1−i3−1+i32−1−i3−1+i30000000000333-1−3−3i32−3+3i32-1-1001+i321−i322−1−i3−1+i32−1−i3−1+i30000000000
χ19333-1−3−3i32−3+3i32-1-1001+i321−i32−1+i32−1−i3−1−i3−1+i320000000000333-1−3−3i32−3+3i32-1-1001+i321−i32−1+i32−1−i3−1−i3−1+i320000000000333-1−3−3i32−3+3i32-1-1001+i321−i32−1+i32−1−i3−1−i3−1+i320000000000
χ20333-1−3−3i32−3+3i32-1-1001+i321−i32−1−i3−1+i32−1+i32−1−i30000000000333-1−3−3i32−3+3i32-1-1001+i321−i32−1−i3−1+i32−1+i32−1−i30000000000333-1−3−3i32−3+3i32-1-1001+i321−i32−1−i3−1+i32−1+i32−1−i30000000000
χ213−3+3i32−3−3i32300−3+3i32−3−3i320000000000ζ+2ζ4ζ−ζ4−2ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ500003−3+3i32−3−3i32300−3+3i32−3−3i320000000000ζ+2ζ4ζ−ζ4−2ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ500003−3+3i32−3−3i32300−3+3i32−3−3i320000000000ζ+2ζ4ζ−ζ4−2ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ50000
χ223−3+3i32−3−3i32300−3+3i32−3−3i320000000000ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ500003−3+3i32−3−3i32300−3+3i32−3−3i320000000000ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ500003−3+3i32−3−3i32300−3+3i32−3−3i320000000000ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ50000
χ233−3+3i32−3−3i32300−3+3i32−3−3i320000000000−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ500003−3+3i32−3−3i32300−3+3i32−3−3i320000000000−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ500003−3+3i32−3−3i32300−3+3i32−3−3i320000000000−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ50000
χ243−3−3i32−3+3i32300−3−3i32−3+3i3200000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ400003−3−3i32−3+3i32300−3−3i32−3+3i3200000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ400003−3−3i32−3+3i32300−3−3i32−3+3i3200000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ40000
χ253−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ400003−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ400003−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ40000
χ263−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ400003−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ400003−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ40000
χ279−9+9i32−9−9i32-3003−3i323+3i32000000000000000000009−9+9i32−9−9i32-3003−3i323+3i32000000000000000000009−9+9i32−9−9i32-3003−3i323+3i3200000000000000000000
χ289−9−9i32−9+9i32-3003+3i323−3i32000000000000000000009−9−9i32−9+9i32-3003+3i323−3i32000000000000000000009−9−9i32−9+9i32-3003+3i323−3i3200000000000000000000
χ291111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ30111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i3211−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i3211−1+i32−1+i32
χ31111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i3211−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i3211
χ3211111111−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+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+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i321−1+i32
χ3311111111−1+i32−1−i3211−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321
χ3411111111−1+i32−1−i3211−1+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−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1−i32111111−1−i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−i321−1+i32−1−i32
χ3511111111−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−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+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321
χ3611111111−1−i32−1+i3211−1−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+i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1+i32111111−1+i32−1+i32−1+i32−1−i32−1+i321−1−i32
χ3711111111−1−i32−1+i3211−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32−1+i32111−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32
χ383333−3+3i32−3−3i323300−3+3i32−3−3i320000000000000000−3+3i32−3+3i32−3+3i32−3+3i32−3−3i323−3+3i32−3+3i3200−3−3i3230000000000000000−3−3i32−3−3i32−3−3i32−3−3i323−3+3i32−3−3i32−3−3i32003−3+3i320000000000000000
χ393333−3−3i32−3+3i323300−3−3i32−3+3i320000000000000000−3+3i32−3+3i32−3+3i32−3+3i323−3−3i32−3+3i32−3+3i32003−3−3i320000000000000000−3−3i32−3−3i32−3−3i32−3−3i32−3+3i323−3−3i32−3−3i3200−3+3i3230000000000000000
χ40333-133-1-133-1-1-1-1-1-1-1-10000000000−3+3i32−3+3i32−3+3i321−i32−3+3i32−3+3i321−i321−i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321−i321−i320000000000−3−3i32−3−3i32−3−3i321+i32−3−3i32−3−3i321+i321+i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321+i321+i320000000000
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χ803−3−3i32−3+3i32300−3−3i32−3+3i3200000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ40000−3−3i32−3+3i323−3−3i3200−3+3i3230000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ40000−3+3i323−3−3i32−3+3i32003−3−3i320000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ40000
χ813−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ40000−3−3i32−3+3i323−3−3i3200−3+3i32300000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ40000−3+3i323−3−3i32−3+3i32003−3−3i320000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ40000
χ823−3−3i32−3+3i32300−3−3i32−3+3i320000000000−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ40000−3−3i32−3+3i323−3−3i3200−3+3i3230000000000−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ40000−3+3i323−3−3i32−3+3i32003−3−3i3200000000002ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ40000
χ839−9+9i32−9−9i32-3003−3i323+3i3200000000000000000000−9−9i329−9+9i323+3i3200-33−3i3200000000000000000000−9+9i32−9−9i3293−3i32003+3i32-300000000000000000000
χ849−9−9i32−9+9i32-3003+3i323−3i3200000000000000000000−9−9i32−9+9i3293+3i32003−3i32-300000000000000000000−9+9i329−9−9i323−3i3200-33+3i3200000000000000000000

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