Finite Group Databasebeta

← Group #13180347

Character table — Group #13180347

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size134439121241216164121616134439121241216164121616268861824248243232824323226886182424824323282432323912129273636123648481236484839121292736361236484812364848
order123322663633363322662266666666663633666636333633666666666666666644121244121212121212121212124412124412121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32
χ311−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32
χ43-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-100
χ511111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ611−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i32
χ711−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i321
χ83-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i3200
χ911111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ1011−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i321
χ1111−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i32
χ123-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i3200
χ133333-1-1-1-1000000003333-1-1-1-1000000003333-1-1-1-1000000003333-1-1-1-1000000003333-1-1-1-1000000003333-1-1-1-100000000
χ1433−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i3200000000
χ1533−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i3200000000
χ169-300-3100000000009-300-3100000000009-300-3100000000009-300-3100000000009-300-3100000000009-300-310000000000
χ171111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1811−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32
χ1911−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32
χ203-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-100-3100-3100-3100-3100-3100-3100-3100-3100
χ2111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32
χ2211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i32-11+i321+i32-11−i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i32-11+i321+i32-11−i32
χ2311−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i32111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i321-1-11+i321−i32-1-11+i321−i321−i321−i32-11+i321+i321+i321−i32-1-1-11+i321−i32-1-11+i321−i321−i321−i32-11+i321+i321+i321−i32-1
χ243-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i32003-1003-100−3+3i321−i3200−3−3i321+i3200-3100-31003−3i32−1+i32003+3i32−1−i3200-3100-31003−3i32−1+i32003+3i32−1−i3200
χ2511111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32
χ2611−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i321-1-11−i321+i32-1-11−i321+i321+i321+i32-11−i321−i321−i321+i32-1-1-11−i321+i32-1-11−i321+i321+i321+i32-11−i321−i321−i321+i32-1
χ2711−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i32-1-11+i321−i32-1-11+i321−i321+i321+i321−i32-11−i321−i32-11+i32-1-11+i321−i32-1-11+i321−i321+i321+i321−i32-11−i321−i32-11+i32
χ283-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i32003-1003-100−3−3i321+i3200−3+3i321−i3200-3100-31003+3i32−1−i32003−3i32−1+i3200-3100-31003+3i32−1−i32003−3i32−1+i3200
χ293333-1-1-1-1000000003333-1-1-1-1000000003333-1-1-1-1000000003333-1-1-1-100000000-3-3-3-3111100000000-3-3-3-3111100000000
χ3033−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i320000000033−3+3i32−3−3i32-1-11−i321+i3200000000-3-33−3i323+3i3211−1+i32−1−i3200000000-3-33−3i323+3i3211−1+i32−1−i3200000000
χ3133−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i320000000033−3−3i32−3+3i32-1-11+i321−i3200000000-3-33+3i323−3i3211−1−i32−1+i3200000000-3-33+3i323−3i3211−1−i32−1+i3200000000
χ329-300-3100000000009-300-3100000000009-300-3100000000009-300-310000000000-93003-10000000000-93003-10000000000
χ331111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ3411−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32iiζ7ζ11iiζ7ζ11iiζ7ζ11iiζ7ζ11−i−i−ζ7−ζ11−i−i−ζ7−ζ11−i−i−ζ7−ζ11−i−i−ζ7−ζ11
χ3511−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32iiζ11ζ7iiζ11ζ7iiζ11ζ7iiζ11ζ7−i−i−ζ11−ζ7−i−i−ζ11−ζ7−i−i−ζ11−ζ7−i−i−ζ11−ζ7
χ363-1003-1003-1003-100-3100-3100-3100-31003-1003-1003-1003-100-3100-3100-3100-31003i−i003i−i003i−i003i−i00−3ii00−3ii00−3ii00−3ii00
χ3711111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32iiiiiiiiζ7ζ7ζ7ζ7ζ11ζ11ζ11ζ11−i−i−i−i−i−i−i−i−ζ7−ζ7−ζ7−ζ7−ζ11−ζ11−ζ11−ζ11
χ3811−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i32-11+i321+i32-11−i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i321−1−i32−1−i321−1+i32-1-11−i321+i32-1-11−i321+i321−i321−i321+i32-11+i321+i32-11−i32iiζ7ζ11iiζ7ζ11ζ7ζ7ζ11iζ11ζ11iζ7−i−i−ζ7−ζ11−i−i−ζ7−ζ11−ζ7−ζ7−ζ11−i−ζ11−ζ11−i−ζ7
χ3911−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i321-1-11+i321−i32-1-11+i321−i321−i321−i32-11+i321+i321+i321−i32-111−1−i32−1+i3211−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1+i321-1-11+i321−i32-1-11+i321−i321−i321−i32-11+i321+i321+i321−i32-1iiζ11ζ7iiζ11ζ7ζ7ζ7iζ11ζ11ζ11ζ7i−i−i−ζ11−ζ7−i−i−ζ11−ζ7−ζ7−ζ7−i−ζ11−ζ11−ζ11−ζ7−i
χ403-1003-100−3+3i321−i3200−3−3i321+i3200-3100-31003−3i32−1+i32003+3i32−1−i32003-1003-100−3+3i321−i3200−3−3i321+i3200-3100-31003−3i32−1+i32003+3i32−1−i32003i−i003i−i003ζ7−ζ7003ζ11−ζ1100−3ii00−3ii00−3ζ7ζ700−3ζ11ζ1100
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χ8922222222−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3-2-2-2-2-2-2-2-21+i31+i31+i31+i31−i31−i31−i31−i3-1-1-1-1-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200000000000000000000000000000000
χ9022−1+i3−1−i322−1+i3−1−i3−1−i3−1−i32−1+i3−1+i3−1+i3−1−i32-2-21−i31+i3-2-21−i31+i31+i31+i3-21−i31−i31−i31+i3-2-1-11−i321+i32-1-11−i321+i321+i321+i32-11−i321−i321−i321+i32-111−1+i32−1−i3211−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1−i32100000000000000000000000000000000
χ9122−1−i3−1+i322−1−i3−1+i3−1−i3−1−i3−1+i32−1+i3−1+i32−1−i3-2-21+i31−i3-2-21+i31−i31+i31+i31−i3-21−i31−i3-21+i3-1-11+i321−i32-1-11+i321−i321+i321+i321−i32-11−i321−i32-11+i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i321−1+i32−1+i321−1−i3200000000000000000000000000000000
χ926-2006-200−3−3i31+i300−3+3i31−i300-6200-62003+3i3−1−i3003−3i3−1+i300-3100-31003+3i32−1−i32003−3i32−1+i32003-1003-100−3−3i321+i3200−3+3i321−i320000000000000000000000000000000000
χ936666-2-2-2-200000000-6-6-6-6222200000000-3-3-3-31111000000003333-1-1-1-10000000000000000000000000000000000000000
χ9466−3+3i3−3−3i3-2-21−i31+i300000000-6-63−3i33+3i322−1+i3−1−i300000000-3-33−3i323+3i3211−1+i32−1−i320000000033−3+3i32−3−3i32-1-11−i321+i320000000000000000000000000000000000000000
χ9566−3−3i3−3+3i3-2-21+i31−i300000000-6-63+3i33−3i322−1−i3−1+i300000000-3-33+3i323−3i3211−1−i32−1+i320000000033−3−3i32−3+3i32-1-11+i321−i320000000000000000000000000000000000000000
χ9618-600-620000000000-186006-20000000000-93003-100000000009-300-31000000000000000000000000000000000000000000

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