Finite Group Databasebeta

← Group #13156606

Character table — Group #13156606

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order122233344666666666333666666666121212121212121212128888366612121212121212122424242424242424242424242424242444442466666666121212121212121212121212888824661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1
χ51111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-111
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χ11222222-12222-1-12-1222-1-12-1-1-1-122-12-122-12-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000020000000022-1-1-1-1-1-10000000020-1-100
χ12222222-12222-1-12-1222-1-12-1-1-1-122-12-122-12-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000-200000000-2-211111100000000-201100
χ13222222-12222-1-12-1222-1-12-1-1-1-122-12-122-12-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-21111111111110000020000000022-1-1-1-1-1-100000000-201100
χ14222222-12222-1-12-1222-1-12-1-1-1-122-12-122-12-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000-200000000-2-21111110000000020-1-100
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χ1722222-12222222-12-1-122-1-122-1-1-1-12-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-22-222-1-1-1-1-1-111-2-2111111110000000000
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χ252222-12222-1-1222222-1-12-1-1-122-1-1-1-12222-1-1-12-1-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-2-2-2-211111111000020-1-122-1-1-1-100000000000000000-20011
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.