Finite Group Databasebeta

← Group #11782801

Character table — Group #11782801

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444444444444444444444444444444444444444444444444443636363636363636484848484848484848484848
order1222334444446666663666888812121212121212121212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424248888888844441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111
χ71111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1
χ922222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000
χ1022222222-2-2-2-22222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222200000000000000000000
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χ14222222-2-2-2-22222222222220000-2-222-2-222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2220000000000000000
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χ1722222-122222222-1-1-12-1-1-1-1-2-2-2-222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-2111111111111000000002-200-1-1110000
χ1822222-122222222-1-1-12-1-1-1-1-2-2-2-222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-211111111111100000000-220011-1-10000
χ1922222-122-2-2-2-222-1-1-12-1-1-1-122-2-2-2-21111-2-21111111122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000−i3i3−i3i30000
χ2022222-122-2-2-2-222-1-1-12-1-1-1-122-2-2-2-21111-2-21111111122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000i3−i3i3−i30000
χ2122222-122-2-2-2-222-1-1-12-1-1-1-1-2-222-2-21111-2-21111111122-1-1-1-1-1-1-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-1000000000000−i3i3i3−i30000
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χ242222-12222222-1-1222-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000-2-200001111
χ252222-12222222-1-1222-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-11111-2-2-2-2111111111111-2-2-2-21111111100000000002-20000-1-111
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χ292222-1222-2-2-2-2-1-1222-1-1-1-1-1-2-22211-2-2-2-21111111111-1-122-1-1-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000−i3i3i3−i3
χ302222-1222-2-2-2-2-1-1222-1-1-1-1-1-2-22211-2-2-2-21111111111-1-122-1-1-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000i3−i3−i3i3
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χ854-44-4-2-2-4400002-222-221-1-11000000000000−3i3i−3i3i3i−3i−3i3i2-22-2-11-11000023−23−2323−33−333−33−32i3−2i3−2i32i30000−i3i3i3−i3i3−i3−i3i300000000000000000000
χ864-44-4-2-2-4400002-222-221-1-11000000000000−3i3i−3i3i3i−3i−3i3i2-22-2-11-110000−232323−233−33−3−33−33−2i32i32i3−2i30000i3−i3−i3i3−i3i3i3−i300000000000000000000
χ874-4-444-200004-4-4-4-2224-2-22222−2222−2200-22004-40000-2-222000000002222−22−22−2−222−2−2−2−222222222−22−22−2−222−2−2−2−2222200000000000000000000
χ884-4-444-200004-4-4-4-2224-2-222−2222−222200-22004-40000-2-22200000000−22−22222222−2−22222−2−2−2−2−22−22222222−2−22222−2−2−2−200000000000000000000
χ894-4-444-20000-44-4-4-2224-2-22222−22−2222002-200-44000022-2-2000000002222−22−22−2−222−2−2−2−22222−22−22222222−2−22222−2−2−2−200000000000000000000
χ904-4-444-20000-44-4-4-2224-2-222−222222−22002-200-44000022-2-200000000−22−22222222−2−22222−2−2−2−22222−22−22−2−222−2−2−2−2222200000000000000000000
χ914-4-44-2400004-4224-4-4-2-2-22222−2222−22004-400-220000-2-22200000000−2−2222222−22−22−2−2−2−22222−2−2222222−22−22−2−2−2−2222200000000000000000000
χ924-4-44-2400004-4224-4-4-2-2-222−2222−2222004-400-220000-2-2220000000022−2−2−22−2222222222−2−2−2−222−2−2−22−2222222222−2−2−2−200000000000000000000
χ934-4-44-240000-44224-4-4-2-2-22222−22−222200-44002-2000022-2-200000000−2−2222222−22−22−2−2−2−2222222−2−2−22−2222222222−2−2−2−200000000000000000000
χ944-4-44-240000-44224-4-4-2-2-222−222222−2200-44002-2000022-2-20000000022−2−2−22−2222222222−2−2−2−2−2−2222222−22−22−2−2−2−2222200000000000000000000
χ954-4-44-2-200004-422-222-211-1-122−2222−2200-2200-223i−3i−3i3i11-1-10000−3i3i3i−3i−2−222−2−222−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ23−2−222−2−222ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000
χ964-4-44-2-200004-422-222-211-1-122−2222−2200-2200-22−3i3i3i−3i11-1-100003i−3i−3i3i−2−222−2−222ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−2−222−2−222−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000
χ974-4-44-2-200004-422-222-211-1-1−2222−222200-2200-223i−3i−3i3i11-1-10000−3i3i3i−3i22−2−222−2−22ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ2322−2−222−2−2−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ2300000000000000000000
χ984-4-44-2-200004-422-222-211-1-1−2222−222200-2200-22−3i3i3i−3i11-1-100003i−3i−3i3i22−2−222−2−2−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ2322−2−222−2−22ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ2300000000000000000000
χ994-4-44-2-20000-4422-222-211-1-122−22−2222002-2002-23i−3i−3i3i-1-11100003i−3i−3i3i−2−222−2−222ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ2322−2−222−2−22ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ2300000000000000000000
χ1004-4-44-2-20000-4422-222-211-1-122−22−2222002-2002-2−3i3i3i−3i-1-1110000−3i3i3i−3i−2−222−2−222−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ2322−2−222−2−2−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ2300000000000000000000
χ1014-4-44-2-20000-4422-222-211-1-1−222222−22002-2002-23i−3i−3i3i-1-11100003i−3i−3i3i22−2−222−2−2−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23−2−222−2−222−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000
χ1024-4-44-2-20000-4422-222-211-1-1−222222−22002-2002-2−3i3i3i−3i-1-1110000−3i3i3i−3i22−2−222−2−22ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2−222−2−222ζ5+2ζ7+ζ13+2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.