Finite Group Databasebeta

← Group #13156579

Character table — Group #13156579

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order122233344666666666333666666666121212121212121212128888366612121212121212122424242424242424242424242424242444442266666666666666661212121288884412121212
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
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111
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
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
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χ11222222-1222222-1-1-1222-1-122-1-1-1-12-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ12222222-1222222-1-1-1222-1-122-1-1-1-12-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-2-2-2-2-2-2111111111111-1-1-1-10000000000
χ13222222-1222222-1-1-1222-1-122-1-1-1-12-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-22-222-2-2-1-111-1-1-1-1111111110000000000
χ14222222-1222222-1-1-1222-1-122-1-1-1-12-1-1-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2-22-2-22211-1-11111-1-1-1-111110000000000
χ15222222-1-2-22222-1-1-1222-1-122-1-1-1-12-1-111-2-2-2-2-2-2-2-20000-1-1-1-111111111000000000000000022-2-2000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3-1-1110000000000
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χ17222222-1-2-22222-1-1-1222-1-122-1-1-1-12-1-111-2-2-2-2-2-2-2-20000-1-1-1-1111111110000000000000000-2-222000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i311-1-10000000000
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χ2022222-122222-1-12222-1-12-1-1-122-1-1-12-1222-1-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000-2001100-2-200001111000000000-20011
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χ412-2-222-122-2-2-2112-2-22-1-12-111-2-211-12-12-2-21112-1-1-1-222-2-111-12-2-11-1-111-222-21-1-1111-1-1-1-11100000000−i3i300000000−i3i3−i3i3000000000000i3−i3
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.