Finite Group Databasebeta

← Group #11782678

Character table — Group #11782678

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444444444444444444444444444444444444444444444444443636363636363636484848484848484848484848
order122233444444666666366688881212121212121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424888888882244666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
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
χ11222222-2-222-2-2222222222200002222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022-2-20000000000000000
χ12222222-2-222-2-2222222222200002222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2220000000000000000
χ13222222-2-2-2-22222222222220000-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000022-2-2000000000000
χ14222222-2-2-2-22222222222220000-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2-222000000000000
χ1522222-122222222-1-12-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000020200-1-100-1-1
χ1622222-122222222-1-12-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000-20-200110011
χ1722222-122222222-1-12-1-1-1-1-1-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111111111-2-2-2-211111111111100000000020-200-1-10011
χ1822222-122222222-1-12-1-1-1-1-1-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111111111-2-2-2-2111111111111000000000-202001100-1-1
χ1922222-122-2-2-2-222-1-12-1-1-1-1-122-2-2-2-211-2-21111111111-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000−i3i300−i3i3
χ2022222-122-2-2-2-222-1-12-1-1-1-1-122-2-2-2-211-2-21111111111-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000i3−i300i3−i3
χ2122222-122-2-2-2-222-1-12-1-1-1-1-1-2-222-2-211-2-21111111111-1-122-1-1-1-1-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-100000000000000−i3i300i3−i3
χ2222222-122-2-2-2-222-1-12-1-1-1-1-1-2-222-2-211-2-21111111111-1-122-1-1-1-1-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-100000000000000i3−i300−i3i3
χ232222-12222222-1-122-12-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000002020-1-100-1-100
χ242222-12222222-1-122-12-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-20-2011001100
χ252222-12222222-1-122-12-1-1-1-1-2-2-2-2-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-2111111110000000020-20-1-1001100
χ262222-12222222-1-122-12-1-1-1-1-2-2-2-2-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-21111111100000000-20201100-1-100
χ272222-1222-2-2-2-2-1-122-12-1-1-1-122-2-211-2-211-2-21111111122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000000−i3i300−i3i300
χ282222-1222-2-2-2-2-1-122-12-1-1-1-122-2-211-2-211-2-21111111122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000000i3−i300i3−i300
χ292222-1222-2-2-2-2-1-122-12-1-1-1-1-2-22211-2-211-2-21111111122-1-1-1-1-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1000000000000−i3i300i3−i300
χ302222-1222-2-2-2-2-1-122-12-1-1-1-1-2-22211-2-211-2-21111111122-1-1-1-1-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1000000000000i3−i300−i3i300
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χ3222-2-222002-2002-22-2-2-222-2-2−i2i2−i2i22-22-2000022-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200-22i2−i2i2−i2000000000000
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χ464444-2-244-4-4-4-4-2-2-2-2-2-21111-4-44422222222-1-1-1-1-1-1-1-1-2-2-2-2111122222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111100000000000000000000
χ474444-2-2-4-444-4-4-2-2-2-2-2-211110000-2-2-2-222221111-1-1-1-12222-1-1-1-1000000003i3i−3i−3i3i3i−3i−3i000000003i3i−3i−3i3i3i−3i−3i00000000000000000000
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χ494444-2-2-4-4-4-444-2-2-2-2-2-2111100002222-2-2-2-2-1-1-1-111112222-1-1-1-1000000003i3i−3i−3i3i3i−3i−3i00000000−3i−3i3i3i−3i−3i3i3i00000000000000000000
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χ5144-4-44-2004-4004-4-22-42-2-222−2i22i2−2i22i24-4-220000-2-222000000000000−2i2−2i22i22i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2i2−2i22i22i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000000000000000
χ5244-4-44-2004-4004-4-22-42-2-2222i2−2i22i2−2i24-4-220000-2-2220000000000002i22i2−2i2−2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22i22i2−2i2−2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.