Finite Group Databasebeta

← Group #10693810

Character table — Group #10693810

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12224444223444444444466612121212661212121212121212121288888888888824242424242424242424242424242424242424242424242488888888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111i−ii−iii−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111i−ii−iii−i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-111
χ111111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111i−ii−i−i−iii-1-111ii−i−iii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-1-111
χ121111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111i−ii−i−i−iii-1-111ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−i−i−iii11-1-1
χ131111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111−ii−iiii−i−i-1-111−i−iii−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-1-111
χ141111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111−ii−iiii−i−i-1-111−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iiiii−i−i11-1-1
χ151111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111−ii−ii−i−iii11-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii11-1-1
χ161111-1-1-1-1111-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-111−ii−ii−i−iii11-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-111
χ172222222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ182222222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
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χ202222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
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χ2622222222-2-22-2-2-2-22222-2-22222222-2-222-2-2-2-222-2-2000000000000000000000000000000000000-2-222-2-222000000000000
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χ3022222222-2-2-1-2-222-2-2-2-222-1-1-1-1-1-1-1111111-1-111-1-1-2-222000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ312222-2-2-2-2222-2-222-2-222-2-2222-2-2-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000002-2-220000
χ322222-2-2-2-2222-2-222-2-222-2-2222-2-2-2-222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000-222-20000
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χ342222-2-2-2-222-1-2-2-2-222-2-222-1-1-11111-1-1-1-1111111-1-12i−2i2i−2i−2i−2i2i2i-2-222−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-100000000000000000000
χ352222-2-2-2-222-1-2-2-2-222-2-222-1-1-11111-1-1-1-1111111-1-1−2i2i−2i2i2i2i−2i−2i-2-222ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-100000000000000000000
χ362222-2-2-2-222-1-2-2-2-222-2-222-1-1-11111-1-1-1-1111111-1-1−2i2i−2i2i−2i−2i2i2i22-2-2ii−i−iii−i−iiiii−i−i−i−i-1-1-1-1111100000000000000000000
χ372222-2-2-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000000000000022-2-2-2-222000000000000
χ382222-2-2-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000-2-22222-2-2000000000000
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χ402222-2-2-2-2-2-2222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-22222−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
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χ432222-2-2-2-2-2-2-122-2-2-2-22222-1-1-111111111-1-111-1-1-1-1−2i2i2i−2i00000000ii−i−i−i−iii33−3−3−3−333i3i3−i3−i3−i3−i3i3i300000000000000000000
χ442222-2-2-2-2-2-2-122-2-2-2-22222-1-1-111111111-1-111-1-1-1-1−2i2i2i−2i00000000ii−i−i−i−iii−3−33333−3−3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ4522-2-22i−2i2i−2i2-222i−2i2i−2i2-22i−2i2-22-2-22i−2i2i−2i2-22-22i−2i2i−2i2i−2i2-200000000000000000000000000000000000000000000000000002i−2i2-2
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χ4722-2-22i−2i2i−2i2-222i−2i−2i2i-22−2i2i-222-2-22i−2i2i−2i2-2-222i−2i−2i2i−2i2i-2200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
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χ5322-2-22i−2i2i−2i-222−2i2i2i−2i-22−2i2i2-22-2-22i−2i2i−2i-22-22−2i2i2i−2i−2i2i2-200000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ5422-2-22i−2i2i−2i-222−2i2i2i−2i-22−2i2i2-22-2-22i−2i2i−2i-22-22−2i2i2i−2i−2i2i2-2000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ5522-2-22i−2i2i−2i-222−2i2i−2i2i2-22i−2i-222-2-22i−2i2i−2i-222-2−2i2i−2i2i2i−2i-22000000002-22i−2i00000000000000002-2-222i−2i−2i2i00000000000000000000
χ5622-2-22i−2i2i−2i-222−2i2i−2i2i2-22i−2i-222-2-22i−2i2i−2i-222-2−2i2i−2i2i2i−2i-2200000000-22−2i2i0000000000000000-222-2−2i2i2i−2i00000000000000000000
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χ6222-2-2−2i2i−2i2i2-22−2i2i2i−2i-222i−2i-222-2-2−2i2i−2i2i2-2-22−2i2i2i−2i2i−2i-2200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
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χ6422-2-2−2i2i−2i2i2-22−2i2i−2i2i2-2−2i2i2-22-2-2−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i2-20000000000000000000000000000000000000000000000000000−2i2i2-2
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χ7122-2-2−2i2i−2i2i-2222i−2i−2i2i-222i−2i2-22-2-2−2i2i−2i2i-22-222i−2i−2i2i2i−2i2-2000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ7222-2-2−2i2i−2i2i-2222i−2i−2i2i-222i−2i2-22-2-2−2i2i−2i2i-22-222i−2i−2i2i2i−2i2-200000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ7322-2-2−2i2i−2i2i-22-12i−2i2i−2i2-2−2i2i-22-111i−ii−i1-1-11−ii−iii−i1-1000000002-2−2i2iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23-111-1i−i−ii00000000000000000000
χ7422-2-2−2i2i−2i2i-22-12i−2i2i−2i2-2−2i2i-22-111i−ii−i1-1-11−ii−iii−i1-1000000002-2−2i2i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23-111-1i−i−ii00000000000000000000
χ7522-2-2−2i2i−2i2i-22-12i−2i2i−2i2-2−2i2i-22-111i−ii−i1-1-11−ii−iii−i1-100000000-222i−2iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ231-1-11−iii−i00000000000000000000
χ7622-2-2−2i2i−2i2i-22-12i−2i2i−2i2-2−2i2i-22-111i−ii−i1-1-11−ii−iii−i1-100000000-222i−2i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ231-1-11−iii−i00000000000000000000
χ774444444444-244-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-222-2-222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-2-4-4-4-44444-4-4-2-2-2-2-2-2-222-2-22222-2-22200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-2-4-444-4-444-4-4-2-2-22222-2-22222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-4-2444444-4-4-4-4-2-2-2222222-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ8144-4-44i−4i4i−4i4-4-24i−4i4i−4i4-44i−4i4-4-222−2i2i−2i2i-22-22−2i2i−2i2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ8244-4-44i−4i4i−4i-44-2−4i4i4i−4i-44−4i4i4-4-222−2i2i−2i2i2-22-22i−2i−2i2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ8344-4-4−4i4i−4i4i4-4-2−4i4i−4i4i4-4−4i4i4-4-2222i−2i2i−2i-22-222i−2i2i−2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ8444-4-4−4i4i−4i4i-44-24i−4i−4i4i-444i−4i4-4-2222i−2i2i−2i2-22-2−2i2i2i−2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ854-44-444-4-40040000000000-44-444-4-40000000000000000000000000000000000000000000000000022−220022−22000000000000
χ864-44-444-4-40040000000000-44-444-4-400000000000000000000000000000000000000000000000000−222200−2222000000000000
χ874-44-4-4-4440040000000000-44-4-4-4440000000000000000000000000000000000000000000000000022−2200−2222000000000000
χ884-44-4-4-4440040000000000-44-4-4-44400000000000000000000000000000000000000000000000000−22220022−22000000000000
χ894-4-444i−4i−4i4i0040000000000-4-444i−4i−4i4i000000000000000000000000000000000000000000000000−2i22i20022−2200000000000000
χ904-4-444i−4i−4i4i0040000000000-4-444i−4i−4i4i0000000000000000000000000000000000000000000000002i2−2i200−222200000000000000
χ914-4-44−4i4i4i−4i0040000000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000−2i22i200−222200000000000000
χ924-4-44−4i4i4i−4i0040000000000-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000002i2−2i20022−2200000000000000
χ938-88-888-8-800-400000000004-44-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8-8-88800-400000000004-4444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888i−8i−8i8i00-4000000000044-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i00-4000000000044-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

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