Finite Group Databasebeta

← Group #13161123

Character table — Group #13161123

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11222222222222222444444444444444444444444444444888888888888888888888888888888888881212242424242424242424242424242424242436363636363636367272108108216
order122333334466666663333666666666666666612121212121212121212266666666666666666666666666121212121212121224666681212121224242424242424244444121212121212248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1
χ611111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-111-1-11
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-111111111-1-1111111-1-111-1
χ922222222-2-2222222222222222222222222222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-200000000000000000002-20000002-2000
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χ4522-22-12-1-12-2-12-1-1-2-22-12-1-11-21111-2-21111-12-1-11-2112-2-12-1-1000i3−i300i3−i3−i3i3i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3-112-2-11-112-2-12-1-101-211i3−i300i3−i3−i3i30000000000000
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χ5222-22-1-1-122-2-1-1-12-2-22-1-1-12111-2111111-2-2-1-1-12111-22-2-1-1-12000−i3i3−i3i3i3−i300−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000-11-11-112-2-22111-20-1-1-12i3−i3i3−i3−i3i3000000000000000
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χ67444-2-2-24-244-2-24-2-2-2-211-21-2-24-21111-2-21111-21-2-24-2-2-2-2-24-24-2-2-2-2-2-244-2-211111111-2-2-2-211111111-2-21100000000000000000000000000000000
χ68444-2-2-24-244-2-24-2-2-2-211-21-2-24-21111-2-21111-21-2-24-2-2-2-2-24-2-4222222-4-422-1-1-1-1-1-1-1-12222-1-1-1-11111-2-21100000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.