Finite Group Databasebeta

← Group #13157114

Character table — Group #13157114

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122444444444488888888888899991818181818181818181836363636363611112244444444448888888888889999181818181818181818183636363636361111224444444444888888888888999918181818181818181818363636363636
order12442433668812121212661212242424242424242422442444444444444488361212612336624241212121266121224242424242424246612126121212121212121212121212122424361212612336624241212121266121224242424242424246612126121212121212121212121212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ31111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-11111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-11111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-1
χ41111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-11111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-11111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-1
χ51111111111-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ61111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1
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χ1611-1-1-111111−ii-1-1-1-1-1-111−i−i−i−iiiii-1-1111-1-1-11111-1-1−iii−ii−i11-1-1-111111−ii-1-1-1-1-1-111−i−i−i−iiiii-1-1111-1-1-11111-1-1−iii−ii−i11-1-1-111111−ii-1-1-1-1-1-111−i−i−i−iiiii-1-1111-1-1-11111-1-1−iii−ii−i
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χ1011111111111-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−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+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+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−i321−i321−i321−i321−i321−i32
χ1021111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ1031111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−iii11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7−1+i32−1+i32
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.