Finite Group Databasebeta

← Group #13164875

Character table — Group #13164875

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134
size11111111111133333333666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666484848484848484848484848484848484848484848484848
order12334466121212129918183636363622222444446666666666121212121212121212121818181818181818181818181818181818181818181818181818181818183636363636363636363636363636363636363636363636363636363636363366999912121212181818183636363636363636
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+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+i32111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+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+i32−1+i32
χ5111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i3211−1−i32−1+i32−1+i321111−1−i32−1−i32
χ6111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i321−1+i32−1+i32−1−i32−1−i321−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i3211
χ7111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−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−i32−1−i32
χ8111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i321−1−i32−1−i32−1+i32−1+i321−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i3211
χ9111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i3211−1+i32−1−i32−1−i321111−1+i32−1+i32
χ101111-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ111111-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ121111-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ131111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ141111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1+i3211−1−i321+i321+i321−i321−i32−1+i3211−1−i321−i321−i32-1-1-1-11+i321+i32
χ151111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1−i32−1+i32−1−i321−1−i32−1+i3211−i321−i321+i321+i321−1−i32−1+i321-1-11+i321+i321−i321−i32-1-1
χ161111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321111−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ171111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1+i32−1−i32−1+i321−1+i32−1−i3211+i321+i321−i321−i321−1+i32−1−i321-1-11−i321−i321+i321+i32-1-1
χ181111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1−i3211−1+i321−i321−i321+i321+i32−1−i3211−1+i321+i321+i32-1-1-1-11−i321−i32
χ19333333333333333333333-1-1-1-1-1-13-1-133-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1000000000000000000000000
χ2033333333333333333333-13-1-1-1-1-1-13-1-1-133-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1000000000000000000000000
χ2133333333333333333333-1-13-1-1-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333000000000000000000000000
χ2233333333333333333333-1-1-13-13-1-1-1-1-1-1-1-1-1-133-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ2333333333333333333333-1-1-1-13-13-1-1-1-1-1-1-1-1-1-1-133-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1000000000000000000000000
χ24333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i323-1-1-1-1-1-13-1-133-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i32000000000000000000000000
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χ26333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-13-1-1-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1331+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i32000000000000000000000000
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Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.