Finite Group Databasebeta

← Group #10945094

Character table — Group #10945094

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order122222223444444444444444466666661212121212121212444444121212121212121212121212121212121212121212121212888888882424242424242424242424242424242422224444444444442244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1
χ6111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11
χ7111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11
χ8111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1
χ911111111111-1-1-1-11111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ1011111111111-1-1-1-11111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1
χ1111111111111-1-1-1-11111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1
χ1211111111111-1-1-1-11111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ1311111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1411111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1511111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1611111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ17222222222-2-2222222222222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ18222222222-2-22222-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ2122222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2322222222-1222222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ2422222222-1222222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-122-2-2-2-22222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-122-2-2-2-22222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-122-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-122-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ2922222222-1-2-2222222222222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−300000000000000000000
χ3022222222-1-2-2222222222222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−33300000000000000000000
χ3122222222-1-2-22222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−33300000000000000000000
χ3222222222-1-2-22222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−300000000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1111111112222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−300000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1111111112222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ37222-2-22-2-222-200002i2i−2i−2i00002-2222-2-2-2-222-2-222-2-2002i−2i00000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000022-2-200002i2i−2i−2i00000000
χ38222-2-22-2-222-200002i2i−2i−2i00002-2222-2-2-2-222-2-222-2-2002i−2i00000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000-2-2220000−2i−2i2i2i00000000
χ39222-2-22-2-222-20000−2i−2i2i2i00002-2222-2-2-2-222-2-222-2-200−2i2i0000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000022-2-20000−2i−2i2i2i00000000
χ40222-2-22-2-222-20000−2i−2i2i2i00002-2222-2-2-2-222-2-222-2-200−2i2i0000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000-2-22200002i2i−2i−2i00000000
χ41222-2-22-2-22-2200002i2i−2i−2i0000-22222-2-2-2-2-2-222-2-22200−2i2i00000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000022-2-200002i2i−2i−2i0000
χ42222-2-22-2-22-2200002i2i−2i−2i0000-22222-2-2-2-2-2-222-2-22200−2i2i00000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000-2-2220000−2i−2i2i2i0000
χ43222-2-22-2-22-220000−2i−2i2i2i0000-22222-2-2-2-2-2-222-2-222002i−2i0000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000022-2-20000−2i−2i2i2i0000
χ44222-2-22-2-22-220000−2i−2i2i2i0000-22222-2-2-2-2-2-222-2-222002i−2i0000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000-2-22200002i2i−2i−2i0000
χ4522-22-2-22-222-22i2i−2i−2i00000000-222-2-222-2-222-2-2-2-2222i−2i00002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000002-22-22i−2i2i−2i0000
χ4622-22-2-22-222-22i2i−2i−2i00000000-222-2-222-2-222-2-2-2-2222i−2i00002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i0000
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χ5022-22-2-22-22-222i2i−2i−2i000000002-22-2-222-2-2-2-22222-2-2−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ5122-22-2-22-22-22−2i−2i2i2i000000002-22-2-222-2-2-2-22222-2-22i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ5222-22-2-22-22-22−2i−2i2i2i000000002-22-2-222-2-2-2-22222-2-22i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000-22-222i−2i2i−2i000000000000
χ5322-2-22-2-222220000000022-2-2-2-22-2-2-2-2222222-2-2-2-200002-2000000000000000022-2-222-2-200000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ5422-2-22-2-222220000000022-2-2-2-22-2-2-2-2222222-2-2-2-200002-2000000000000000022-2-222-2-20000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ5522-2-22-2-2222200000000-2-222-2-22-2-2-2-2222222-2-2-2-20000-220000000000000000-2-222-2-22200000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ5622-2-22-2-2222200000000-2-222-2-22-2-2-2-2222222-2-2-2-20000-220000000000000000-2-222-2-2220000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
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χ5822-2-22-2-222-2-20000000022-2-2222-2-2-2-222-2-2-2-222220000-22000000000000000022-2-2-2-222000000000000000000000000-222-2000000002-2-220000
χ5922-2-22-2-222-2-200000000-2-222222-2-2-2-222-2-2-2-2222200002-20000000000000000-2-22222-2-20000000000000000000000002-2-22000000002-2-220000
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χ642-2-2-2-22222002-22-2-22-22-22-2200-22-22-22-2000000000000002-22-20000-22-220000-22-220000−22−222−22−2−22−22−22−222−22−22−22−200000000000000000000
χ652-2-2-2-2222200-22-222-22-2-22-2200-22-22-22-200000000000000-22-2200002-22-20000-22-2200002−2−222−2−222−22−2−22−222−22−2−22−2200000000000000000000
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χ742-2-2-2-2222-1002-22-2-22-22-22-22001-11-11-113−33−33−33−3000000-11-113−33−31-11-1−33−331-11-1−33−33−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ752-2-2-2-2222-1002-22-2-22-22-22-22001-11-11-11−33−33−33−33000000-11-11−33−331-11-13−33−31-11-13−33−32−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
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χ85444-4-44-4-4-24-400004i4i−4i−4i00004-4-2-2-22222-2-222-2-222004i−4i0000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
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χ1094-4-4444-4-440000004i−4i−4i4i000000-44-4-44-4400000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
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χ1144-4-4444-4-4-2000000−4i4i4i−4i0000002-222-22-2−232323−23−232323−23000000000000002i−2i−2i2i2i3−2i3−2i32i30000000000000000000000000000000000000000000000000000

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