Finite Group Databasebeta

← Group #10691273

Character table — Group #10691273

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order12224444223444444666888888881212121244668888121212121212121212122424242424242424242424242424242422444444888888884488121212122424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-1-1-11-1-1-1ii−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-1-1-11-1-1-1ii−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-1-1-11-1-1-1ii−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i−i−iii-1-111
χ121111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-1-1-11-1-1-1ii−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii-11−ii-1-111−i−iiiii−i−i11-1-1
χ131111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-1-1-11-1-1-1−i−iii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii−i−iii11-1-1
χ141111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-1-1-11-1-1-1−i−iii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−iii−i−i-1-111
χ151111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-1-1-11-1-1-1−i−iii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iiiii−i−i-1-111
χ161111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-1-1-11-1-1-1−i−iii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i−i−iii11-1-1
χ17222222222222-2-2-2-22222000000002222-2-222000022-2-2-2-2-2-2-2-200000000000000002222-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-22222000000002222-2-222000022-2-2-2-2-2-2-2-20000000000000000-2-2-2-222220000000000000000000000000000
χ192222222222-1222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ202222222222-1222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ212222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-1111100000000
χ222222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-100000000
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χ2422222222-2-22-22222-2222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
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χ2722222222-2-2-1-22222-2-1-1-122222222-1-1-1-1-2-211-2-2-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2822222222-2-2-1-22222-2-1-1-122222222-1-1-1-1-2-211-2-2-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ2922222222-2-2-1-22222-2-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-211222211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ3022222222-2-2-1-22222-2-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-211222211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
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χ322222-2-2-2-2222-222-2-2-2222−2i−2i−2i−2i2i2i2i2i-2-2-2-2-22222i2i−2i−2i-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
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χ362222-2-2-2-222-1-222-2-2-2-1-1-12i2i2i2i−2i−2i−2i−2i1111-22-1-1−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000i3−i3−i3i3−333−300000000
χ372222-2-2-2-222-1-222-2-2-2-1-1-1−2i−2i−2i−2i2i2i2i2i1111-22-1-12i2i−2i−2i11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−i3i3i3−i3−333−300000000
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χ402222-2-2-2-2-2-222-2-222222200000000-2-2-2-2-22-2-2000022-2-2-2-222220000000000000000-2-22222-2-20000000000000000000000000000
χ412222-2-2-2-2-2-2-1222-2-22-1-1-12i2i2i2i−2i−2i−2i−2i11112-2112i2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i-1-111−i−iii00000000
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χ432222-2-2-2-2-2-2-1222-2-22-1-1-1−2i−2i−2i−2i2i2i2i2i11112-211−2i−2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i00000000
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χ4522-2-222-2-22-2220000-22-2-222−2−222−2−222-2-2002-22−22−22-20000000022−2−222−2−222−2−222−2−22-22-200002−22−22−22−200000000000000000000
χ4622-2-222-2-22-2220000-22-2-222−2−222−2−222-2-2002-22−22−22-20000000022−2−222−2−222−2−222−2−2-22-220000−22−22−22−2200000000000000000000
χ4722-2-222-2-22-2220000-22-2-2−2−222−2−22222-2-2002-2−22−222-200000000−2−222−2−222−2−222−2−2222-22-20000−22−22−22−2200000000000000000000
χ4822-2-222-2-22-2220000-22-2-2−2−222−2−22222-2-2002-2−22−222-200000000−2−222−2−222−2−222−2−222-22-2200002−22−22−22−200000000000000000000
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χ622-22-22i−2i2i−2i00202-22i−2i0-22-22ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i00000000002-200002i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000−1−i1+i−1+i1−i−22i2−i2
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χ642-22-22i−2i2i−2i00202-22i−2i0-22-2−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i00000000002-200002i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000−1−i1+i−1+i1−i2−2−i2i2
χ652-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i00000000002-20000−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000001−i−1+i1+i−1−i2−2i2−i2
χ662-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i00000000002-20000−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000−1+i1−i−1−i1+i−22−i2i2
χ672-22-2−2i2i−2i2i00202-2−2i2i0-22-22ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2i2i−2i2i00000000002-20000−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000001−i−1+i1+i−1−i−22−i2i2
χ682-22-2−2i2i−2i2i00202-2−2i2i0-22-22ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2i2i−2i2i00000000002-20000−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000−1+i1−i−1−i1+i2−2i2−i2
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.