Finite Group Databasebeta

← Group #13152250

Character table — Group #13152250

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11111111111133333333121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212484848484848484848484848484848484848484848484848
order12223366666699181818181818224446666121212121212181818181818181818181818363636363636363636363636363636363636336666669999181818181818181818181818
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ311111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−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−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ5111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i32111111−1+i32−1+i32−1+i32
χ6111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−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−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111
χ7111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+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+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ8111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+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+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111
χ9111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i32111111−1−i32−1−i32−1−i32
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χ1333333333333333333333-1-1-13-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1333-1-1-1000000000000000000000000
χ1433333333333333333333-1-1-1-13-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1333000000000000000000000000
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χ263333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32000000003-1-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321+i321−i321+i320002ζ2ζ42ζ70002ζ22ζ52ζ82ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ8000000000000000000000000
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χ313333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000-13-1-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321+i321−i321+i322ζ72ζ2ζ40002ζ52ζ82ζ20002ζ72ζ2ζ42ζ2ζ42ζ72ζ42ζ72ζ2ζ52ζ82ζ22ζ22ζ52ζ82ζ82ζ22ζ5000000000000000000000000
χ323333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000-1-13-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321+i321−i321+i322ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ80002ζ72ζ2ζ42ζ42ζ72ζ0002ζ52ζ82ζ22ζ82ζ22ζ5000000000000000000000000
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χ343333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000-1-13-1-11−i321+i321−i321+i32−3+3i32−3−3i321−i321+i321−i321+i322ζ72ζ2ζ42ζ72ζ2ζ42ζ52ζ82ζ22ζ52ζ82ζ20002ζ42ζ72ζ2ζ2ζ42ζ70002ζ82ζ22ζ52ζ22ζ52ζ8000000000000000000000000
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χ363333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000-1-1-13-11−i321+i321−i321+i321−i321+i32−3+3i32−3−3i321−i321+i322ζ42ζ72ζ2ζ72ζ2ζ42ζ82ζ22ζ52ζ52ζ82ζ22ζ2ζ42ζ70002ζ42ζ72ζ2ζ22ζ52ζ80002ζ82ζ22ζ5000000000000000000000000
χ373333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000-1-1-13-11−i321+i321−i321+i321−i321+i32−3+3i32−3−3i321−i321+i322ζ72ζ2ζ42ζ2ζ42ζ72ζ52ζ82ζ22ζ22ζ52ζ82ζ42ζ72ζ0002ζ72ζ2ζ42ζ82ζ22ζ50002ζ52ζ82ζ2000000000000000000000000
χ383333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000-1-1-1-131−i321+i321−i321+i321−i321+i321−i321+i32−3+3i32−3−3i322ζ2ζ42ζ72ζ72ζ2ζ42ζ22ζ52ζ82ζ52ζ82ζ22ζ42ζ72ζ2ζ2ζ42ζ70002ζ82ζ22ζ52ζ22ζ52ζ8000000000000000000000000000
χ393333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i3200000000-1-1-1-131−i321+i321−i321+i321−i321+i321−i321+i32−3+3i32−3−3i322ζ42ζ72ζ2ζ2ζ42ζ72ζ82ζ22ζ52ζ22ζ52ζ82ζ72ζ2ζ42ζ42ζ72ζ0002ζ52ζ82ζ22ζ82ζ22ζ5000000000000000000000000000
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χ413333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i320000000033333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000000000000000000000
χ423333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000003-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321−i321+i321−i320002ζ22ζ82ζ50002ζ42ζ2ζ72ζ22ζ82ζ52ζ22ζ82ζ52ζ22ζ82ζ52ζ42ζ2ζ72ζ42ζ2ζ72ζ42ζ2ζ7000000000000000000000000
χ433333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000003-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321−i321+i321−i320002ζ52ζ22ζ80002ζ2ζ72ζ42ζ52ζ22ζ82ζ52ζ22ζ82ζ52ζ22ζ82ζ2ζ72ζ42ζ2ζ72ζ42ζ2ζ72ζ4000000000000000000000000
χ443333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32000000003-1-1-1-1−3−3i32−3+3i321+i321−i321+i321−i321+i321−i321+i321−i320002ζ82ζ52ζ20002ζ72ζ42ζ2ζ82ζ52ζ22ζ82ζ52ζ22ζ82ζ52ζ22ζ72ζ42ζ2ζ72ζ42ζ2ζ72ζ42ζ000000000000000000000000
χ453333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i3200000000-13-1-1-11+i321−i32−3−3i32−3+3i321+i321−i321+i321−i321+i321−i322ζ22ζ82ζ50002ζ42ζ2ζ70002ζ22ζ82ζ52ζ82ζ52ζ22ζ52ζ22ζ82ζ42ζ2ζ72ζ72ζ42ζ2ζ2ζ72ζ4000000000000000000000000
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.