Finite Group Databasebeta

← Group #72344019

Character table — Group #72344019

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size111133334444666666661212121212121212121212121212121212121212242424242424242464646464646464646464646464646464111133334444666666661212121212121212121212121212121212121212242424242424242464646464646464646464646464646464
order124422442244222244442222222222444444444444444444336666661212121212121212224422442244222244442222222222444444444444444444666666661212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1
χ511111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ611111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
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χ811-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
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χ1011-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-111
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.