Finite Group Databasebeta

← Group #11782000

Character table — Group #11782000

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222222244444444444444444444444444444444444444444444444444444444444444424242424242424242424242448484848484872727272
order1222334444666666121212123466688881212121212121212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424248888242424242424242444121212122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ71111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ81111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ92222222-2-22222222-2-2-2-22-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ102222222-2-22222222-2-2-2-22-2222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222220000000000000000000000
χ11222222-222-222222222222-2222000022-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000002-200
χ12222222-222-222222222222-2222000022-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000-2200
χ13222222-2-2-2-2222222-2-2-2-2222220000-2-22222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000002i−2i
χ14222222-2-2-2-2222222-2-2-2-2222220000-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000−2i2i
χ1522222-12222222-1-1-12222-12-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
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χ1722222-12222222-1-1-12222-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-21111111111110000000000002-2-1-1110000
χ1822222-12222222-1-1-12222-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-2111111111111000000000000-2211-1-10000
χ1922222-12-2-22222-1-1-1-2-2-2-2-1-2-1-1-122-2-211-2-2111111111122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000−i3i3−i3i30000
χ2022222-12-2-22222-1-1-1-2-2-2-2-1-2-1-1-122-2-211-2-2111111111122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000i3−i3i3−i30000
χ2122222-12-2-22222-1-1-1-2-2-2-2-1-2-1-1-1-2-22211-2-2111111111122-1-1-1-1-1-1-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-100000000000000−i3i3i3−i30000
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χ252222-122222-1-1-1222-1-1-1-1-12-1-1-1-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-11111-2-2-2-2111111111111-2-2-2-21111111122-2-2-1-1-1-111110000000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-1-2-2-2-222-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-11111-2-2-2-2111111111111-2-2-2-211111111-2-2221111-1-1-1-10000000000
χ272222-122-2-22-1-1-12221111-1-2-1-1-122-2-2-2-211-2-211111111-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-211111111000033−3−333−3−30000000000
χ282222-122-2-22-1-1-12221111-1-2-1-1-122-2-2-2-211-2-211111111-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-2111111110000−3−333−3−3330000000000
χ292222-122-2-22-1-1-12221111-1-2-1-1-1-2-222-2-211-2-211111111-1-122-1-1-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1000033−3−3−3−3330000000000
χ302222-122-2-22-1-1-12221111-1-2-1-1-1-2-222-2-211-2-211111111-1-122-1-1-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-10000−3−33333−3−30000000000
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χ362-22-2-12-2002-1112-2-233−3−3-10-111002-2003−30033−3−333−3−3-112-2-1-11133−3−300003333−3−3−3−3-1-11122-2-2-1-1-1-11111i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000
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χ382-22-2-12-2002-1112-2-233−3−3-10-11100-22003−30033−3−333−3−3-112-2-1-111−3−3330000−3−3−3−3333311-1-1-2-2221111-1-1-1-1i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000
χ392-22-2-12-2002-1112-2-2−3−333-10-111002-200−3300−3−333−3−333-112-2-1-111−3−3330000−3−3−3−33333-1-11122-2-2-1-1-1-11111−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
χ402-22-2-12-2002-1112-2-2−3−333-10-111002-200−3300−3−333−3−333-112-2-1-111−3−3330000−3−3−3−33333-1-11122-2-2-1-1-1-11111i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ412-22-2-12-2002-1112-2-2−3−333-10-11100-2200−3300−3−333−3−333-112-2-1-11133−3−300003333−3−3−3−311-1-1-2-2221111-1-1-1-1−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000
χ422-22-2-12-2002-1112-2-2−3−333-10-11100-2200−3300−3−333−3−333-112-2-1-11133−3−300003333−3−3−3−311-1-1-2-2221111-1-1-1-1i2−i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000
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χ514444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-41110000-2-222221111-1-1-1-12222-1-1-1-1000000003i3i−3i−3i3i3i−3i−3i000000003i3i−3i−3i3i3i−3i−3i0000000000000000000000
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χ1044-4-44-2-2000022-222-2−232323−2310-1-11−2222000000−2i32i33−3−33i3−i3−i3i30000−3i3i3i−3i2−2−222−2−22−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.