Finite Group Databasebeta

← Group #13181518

Character table — Group #13181518

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size112222244444444444444488888888888888888899181818181827272727363636545454545454112222244444444444444488888888888888888899181818181827272727363636545454545454
order1234446333333666666121212121212121212121212121212121212121212442221212888866688888822644466666666666661212121212121212121212121212121212121212124422212128888666888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1ii−i−i-1-1-1iii−i−i−i1111111111111111111111111111111111111111-1-1-1-1-1-1-1ii−i−i-1-1-1iii−i−i−i
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1−i−iii-1-1-1−i−i−iiii1111111111111111111111111111111111111111-1-1-1-1-1-1-1−i−iii-1-1-1−i−i−iiii
χ51111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-11-1-11-1-11111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-11-1-11-1-1
χ61111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-11-1-1-111-1111111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-11-1-1-111-111
χ71111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i-111i−i−i−iii1111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i-111i−i−i−iii
χ81111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii-111−iiii−i−i1111-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii-111−iiii−i−i
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.