Finite Group Databasebeta

← Group #13156605

Character table — Group #13156605

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order122233344666666666333666666666121212121212121212128888366612121212121212122424242424242424242424242424242488882266666666666666662424242444444412121212
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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χ12222222-1222222-1-1-1222-1-122-1-1-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-2-2-2-2-2-2111111111111-1-1-1-10000000000
χ13222222-1222222-1-1-1222-1-122-1-1-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-22-222-2-2-1-111-1-1-1-1111111110000000000
χ14222222-1222222-1-1-1222-1-122-1-1-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2-22-2-22211-1-11111-1-1-1-111110000000000
χ1522222-122222-1-12222-1-12-1-1-122-1-1-12-122-1-1-12-1-1-122222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000200-1-100220000-1-1-1-1000000000200-1-1
χ1622222-122222-1-12222-1-12-1-1-122-1-1-12-122-1-1-12-1-1-122222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000-2001100-2-200001111000000000-20011
χ1722222-122222-1-12222-1-12-1-1-122-1-1-12-122-1-1-12-1-1-12-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000200-1-100220000-1-1-1-1000000000-20011
χ1822222-122222-1-12222-1-12-1-1-122-1-1-12-122-1-1-12-1-1-12-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000-2001100-2-200001111000000000200-1-1
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χ202222-12222-1-122222-12-1-12-1-1-1-122-1-122-12-1-1-12-1-122222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-201100-2-2001111000000000000-201100
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χ412-2-222-122-2-2-211-2-222-1-12-111-2-211-12-12-21112-1-1-1-2-222-2-111-12-2-11-1-111-222-21-1-1111-1-1-1-11100000000−i3i300000000−i3i3−i3i3000000000000i3−i3
χ422-2-222-122-2-2-211-2-222-1-12-111-2-211-12-12-21112-1-1-1-2-222-2-111-12-2-11-1-111-222-21-1-1111-1-1-1-11100000000i3−i300000000i3−i3i3−i3000000000000−i3i3
χ432-2-22-1222-211-2-2-2-22-12-1-121111-2-2-1-1221-211-12-1-1-22-2-22-111-1-112-2-1-111-111-12-2-22-1-11111-1-1000000−i3i3000000−i3i3−i3i300000000000000−i3i300
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χ854-4-444-2-24-4-4-42222-24-2-2-212222-1-1-2-21-2-42224-2-2-2200001-1-11-221-111-1-10000000000000000000000002i3−2i300000000−i3i3−i3i300000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.