Finite Group Databasebeta

← Group #66403

Character table — Group #66403

Order 324.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111333333331113333333322266666666222666666663339999999933399999999
order13333999999266661818181818183333399999966666181818181818412121212363636363636412121212363636363636
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ311111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ5111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32
χ6111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321
χ7111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ8111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321
χ9111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32
χ103−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i3200000000
χ113−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i3200000000
χ1211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1311111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1-1-11−i321−i321−i321+i321+i321+i32
χ1411111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1-1-11+i321+i321+i321−i321−i321−i32
χ15111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-11−i321+i32-11−i321+i32-11−i321+i32-1-1-11−i321+i32-11−i321+i32-11−i321+i32
χ16111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1-1-11−i321+i321−i321+i32-11+i32-11−i32-1-1-11−i321+i321−i321+i32-11+i32-11−i32
χ17111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1-1-11−i321+i321+i32-11−i321−i321+i32-1-1-1-11−i321+i321+i32-11−i321−i321+i32-1
χ18111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-11+i321−i32-11+i321−i32-11+i321−i32-1-1-11+i321−i32-11+i321−i32-11+i321−i32
χ19111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1-1-11+i321−i321−i32-11+i321+i321−i32-1-1-1-11+i321−i321−i32-11+i321+i321−i32-1
χ20111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1-1-11+i321−i321+i321−i32-11−i32-11+i32-1-1-11+i321−i321+i321−i32-11−i32-11+i32
χ213−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i32000000003−3+3i32−3−3i3200000000-33−3i323+3i3200000000-33−3i323+3i3200000000
χ223−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i32000000003−3−3i32−3+3i3200000000-33+3i323−3i3200000000-33+3i323−3i3200000000
χ2311111111111-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i
χ2411111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321+i321+i321+i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321+i321+i321+i32iiiiiζ7ζ7ζ7ζ11ζ11ζ11−i−i−i−i−i−ζ7−ζ7−ζ7−ζ11−ζ11−ζ11
χ2511111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321−i321−i321−i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321−i321−i321−i32iiiiiζ11ζ11ζ11ζ7ζ7ζ7−i−i−i−i−i−ζ11−ζ11−ζ11−ζ7−ζ7−ζ7
χ26111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-11−i321+i32-11−i321+i32-11−i321+i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-11−i321+i32-11−i321+i32-11−i321+i32iiiζ7ζ11iζ7ζ11iζ7ζ11−i−i−i−ζ7−ζ11−i−ζ7−ζ11−i−ζ7−ζ11
χ27111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1-1-11−i321+i321−i321+i32-11+i32-11−i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1-1-11−i321+i321−i321+i32-11+i32-11−i32iiiζ7ζ11ζ7ζ11iζ11iζ7−i−i−i−ζ7−ζ11−ζ7−ζ11−i−ζ11−i−ζ7
χ28111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1-1-11−i321+i321+i32-11−i321−i321+i32-1111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1-1-11−i321+i321+i32-11−i321−i321+i32-1iiiζ7ζ11ζ11iζ7ζ7ζ11i−i−i−i−ζ7−ζ11−ζ11−i−ζ7−ζ7−ζ11−i
χ29111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-11+i321−i32-11+i321−i32-11+i321−i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-11+i321−i32-11+i321−i32-11+i321−i32iiiζ11ζ7iζ11ζ7iζ11ζ7−i−i−i−ζ11−ζ7−i−ζ11−ζ7−i−ζ11−ζ7
χ30111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1-1-11+i321−i321−i32-11+i321+i321−i32-1111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1-1-11+i321−i321−i32-11+i321+i321−i32-1iiiζ11ζ7ζ7iζ11ζ11ζ7i−i−i−i−ζ11−ζ7−ζ7−i−ζ11−ζ11−ζ7−i
χ31111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1-1-11+i321−i321+i321−i32-11−i32-11+i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1-1-11+i321−i321+i321−i32-11−i32-11+i32iiiζ11ζ7ζ11ζ7iζ7iζ11−i−i−i−ζ11−ζ7−ζ11−ζ7−i−ζ7−i−ζ11
χ323−3+3i32−3−3i3200000000-33−3i323+3i32000000003−3+3i32−3−3i3200000000-33−3i323+3i32000000003i3ζ73ζ1100000000−3i−3ζ7−3ζ1100000000
χ333−3−3i32−3+3i3200000000-33+3i323−3i32000000003−3−3i32−3+3i3200000000-33+3i323−3i32000000003i3ζ113ζ700000000−3i−3ζ11−3ζ700000000
χ3411111111111-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiii
χ3511111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321+i321+i321+i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321+i321+i321+i32−i−i−i−i−i−ζ7−ζ7−ζ7−ζ11−ζ11−ζ11iiiiiζ7ζ7ζ7ζ11ζ11ζ11
χ3611111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321−i321−i321−i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321−i321−i321−i32−i−i−i−i−i−ζ11−ζ11−ζ11−ζ7−ζ7−ζ7iiiiiζ11ζ11ζ11ζ7ζ7ζ7
χ37111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-11−i321+i32-11−i321+i32-11−i321+i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-11−i321+i32-11−i321+i32-11−i321+i32−i−i−i−ζ7−ζ11−i−ζ7−ζ11−i−ζ7−ζ11iiiζ7ζ11iζ7ζ11iζ7ζ11
χ38111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1-1-11−i321+i321−i321+i32-11+i32-11−i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32-1-1-11−i321+i321−i321+i32-11+i32-11−i32−i−i−i−ζ7−ζ11−ζ7−ζ11−i−ζ11−i−ζ7iiiζ7ζ11ζ7ζ11iζ11iζ7
χ39111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1-1-11−i321+i321+i32-11−i321−i321+i32-1111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321-1-1-11−i321+i321+i32-11−i321−i321+i32-1−i−i−i−ζ7−ζ11−ζ11−i−ζ7−ζ7−ζ11−iiiiζ7ζ11ζ11iζ7ζ7ζ11i
χ40111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-11+i321−i32-11+i321−i32-11+i321−i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-11+i321−i32-11+i321−i32-11+i321−i32−i−i−i−ζ11−ζ7−i−ζ11−ζ7−i−ζ11−ζ7iiiζ11ζ7iζ11ζ7iζ11ζ7
χ41111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1-1-11+i321−i321−i32-11+i321+i321−i32-1111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321-1-1-11+i321−i321−i32-11+i321+i321−i32-1−i−i−i−ζ11−ζ7−ζ7−i−ζ11−ζ11−ζ7−iiiiζ11ζ7ζ7iζ11ζ11ζ7i
χ42111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1-1-11+i321−i321+i321−i32-11−i32-11+i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32-1-1-11+i321−i321+i321−i32-11−i32-11+i32−i−i−i−ζ11−ζ7−ζ11−ζ7−i−ζ7−i−ζ11iiiζ11ζ7ζ11ζ7iζ7iζ11
χ433−3+3i32−3−3i3200000000-33−3i323+3i32000000003−3+3i32−3−3i3200000000-33−3i323+3i3200000000−3i−3ζ7−3ζ11000000003i3ζ73ζ1100000000
χ443−3−3i32−3+3i3200000000-33+3i323−3i32000000003−3−3i32−3+3i3200000000-33+3i323−3i3200000000−3i−3ζ11−3ζ7000000003i3ζ113ζ700000000
χ452222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ4622222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-1-1-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1-1-11−i321−i321−i321+i321+i321+i320000000000000000000000
χ4722222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-1-1-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1-1-11+i321+i321+i321−i321−i321−i320000000000000000000000
χ48222−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3222−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-1-1-11−i321+i32-11−i321+i32-11−i321+i32-1-1-11−i321+i32-11−i321+i32-11−i321+i320000000000000000000000
χ49222−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3222−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3-1-1-11−i321+i321−i321+i32-11+i32-11−i32-1-1-11−i321+i321−i321+i32-11+i32-11−i320000000000000000000000
χ50222−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32222−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32-1-1-11−i321+i321+i32-11−i321−i321+i32-1-1-1-11−i321+i321+i32-11−i321−i321+i32-10000000000000000000000
χ51222−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3222−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-1-1-11+i321−i32-11+i321−i32-11+i321−i32-1-1-11+i321−i32-11+i321−i32-11+i321−i320000000000000000000000
χ52222−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32222−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32-1-1-11+i321−i321−i32-11+i321+i321−i32-1-1-1-11+i321−i321−i32-11+i321+i321−i32-10000000000000000000000
χ53222−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3222−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3-1-1-11+i321−i321+i321−i32-11−i32-11+i32-1-1-11+i321−i321+i321−i32-11−i32-11+i320000000000000000000000
χ546−3+3i3−3−3i3000000006−3+3i3−3−3i300000000-33−3i323+3i3200000000-33−3i323+3i32000000000000000000000000000000
χ556−3−3i3−3+3i3000000006−3−3i3−3+3i300000000-33+3i323−3i3200000000-33+3i323−3i32000000000000000000000000000000
χ5622222222222-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111111110000000000000000000000
χ5722222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2-2-2-2-21−i31−i31−i31+i31+i31+i3-1-1-1-1-11−i321−i321−i321+i321+i321+i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000000000000000000000
χ5822222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2-2-2-2-21+i31+i31+i31−i31−i31−i3-1-1-1-1-11+i321+i321+i321−i321−i321−i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000000000000000000000
χ59222−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3-2-2-21−i31+i3-21−i31+i3-21−i31+i3-1-1-11−i321+i32-11−i321+i32-11−i321+i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i320000000000000000000000
χ60222−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3-2-2-21−i31+i31−i31+i3-21+i3-21−i3-1-1-11−i321+i321−i321+i32-11+i32-11−i32111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i320000000000000000000000
χ61222−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32-2-2-21−i31+i31+i3-21−i31−i31+i3-2-1-1-11−i321+i321+i32-11−i321−i321+i32-1111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i3210000000000000000000000
χ62222−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-2-2-21+i31−i3-21+i31−i3-21+i31−i3-1-1-11+i321−i32-11+i321−i32-11+i321−i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i320000000000000000000000
χ63222−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32-2-2-21+i31−i31−i3-21+i31+i31−i3-2-1-1-11+i321−i321−i32-11+i321+i321−i32-1111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i3210000000000000000000000
χ64222−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3-2-2-21+i31−i31+i31−i3-21−i3-21+i3-1-1-11+i321−i321+i321−i32-11−i32-11+i32111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i320000000000000000000000
χ656−3+3i3−3−3i300000000-63−3i33+3i300000000-33−3i323+3i32000000003−3+3i32−3−3i32000000000000000000000000000000
χ666−3−3i3−3+3i300000000-63+3i33−3i300000000-33+3i323−3i32000000003−3−3i32−3+3i32000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.