Finite Group Databasebeta

← Group #10702088

Character table — Group #10702088

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121244444444666612121212121212121212121212121212121212122244666688881212121224242424242424242244888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
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χ161-1-1111-1-1111-1-1-1111-11-1-111-1-1-1-111111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111ii−i−i-1-111iiii−i−i−i−i-11-11ii−i−i11-1-1−i−iii
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
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χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
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χ2922222222-2-22-2-222-2-2-22-22-2-222-2-2222-2-222-2-200000000-22-22-22-220000000000000000000000000000000000000000000000002-22-20000
χ3022222222-2-22-2-222-2-2-22-22-2-222-2-2222-2-222-2-200000000-22-22-22-22000000000000000000000000000000000000000000000000-22-220000
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χ402222-2-2-2-2-22-2-22-222-222-22-2-222-2-22-2-222-2-222000000002-22-2-22-220000000000000000000000000000000000000000-2-222000000000000
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χ422222-2-2-2-2-2-22-2-222222-22-2-2-222-2-22-2-222-2-222-2-222-2-222-22-222-22-2-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ432222-2-2-2-2-2-22-2-22-1222-22-211-1-111-111-1-111-1-122-2-222-2-21-11-1-11-11-1-11111-1-1-1-11111-1-10000−i3i3−i3i30000i3−i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.