Finite Group Databasebeta

← Group #10702099

Character table — Group #10702099

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12224444222222344444466666661212121212121212444444446666121212121212121212121212121212121212121288888888242424242424242424242424242424242222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
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χ111-1-1111-1-1111-1-1-1111-1-1-1111-1-11-1-111-1-111-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-111111-1-111-1-11ii−i−i−i−iii
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χ161-1-1111-1-1111-1-1-1111-1-1-1111-1-11-1-111-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1-11-11-11-11ii−i−iii−i−i
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
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χ2722222222-22-2-22-222-2-22-2-2-2-2-2-222222-2-2-2-222000000002-22-22-22-200000000000000000000000000000000000000000000000000002-22-2
χ2822222222-22-2-22-222-2-22-2-2-2-2-2-222222-2-2-2-222000000002-22-22-22-20000000000000000000000000000000000000000000000000000-22-22
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χ322222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
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χ362222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222-1-1-1-1111111-1-111-1-111-1-111-1-100000000−33−33−33−333−33−33−33−30000000000000000
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χ472-2-2222-2-2222-2-2-2-122-2-2-22-1-111-111-1-111-1-1112i2i2i2i−2i−2i−2i−2i-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii2i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-111110000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.