Finite Group Databasebeta

← Group #10772493

Character table — Group #10772493

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222223444444446661212121244668888888812121212121212121212242424242424242424242424242424242444224468812121224242424244444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111111-1-11-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-111-1111111-1-1
χ91111-1-11-1-11-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-11-1-111-1-1-1111-1-111-1-11-1
χ101111-1-11-1-11-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111-1-11-1-1-111-1-111-11
χ111111-1-11-1-11-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-111-1-1-111111-1-1-11
χ121111-1-11-1-11-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-111-1-111111-1-1-1-1-1111-1
χ131111-1-11-1-11-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11-111-1-1-1-111-1111-1-1-1-111-11
χ141111-1-11-1-11-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-111-1-1-1-1111-1-1-11111-1-11-1
χ151111-1-11-1-11-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-1-11111-1-1-1-1-1111-1-1111-1
χ161111-1-11-1-11-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-11-1-11111-1-1111-1-1-111-1-1-11
χ17222222222-2-2-2-2-2-2222-2-2-2-2-222200000000-2-222-2-2-2-222000000000000000000000000000000000002-202-2000000
χ18222222222-2-2-2-2-2-2222-2-2-2-2-222200000000-2-222-2-2-2-22200000000000000000000000000000000000-220-22000000
χ192222222-2-2222-2-22222-2-2-2-2-2-2220000000022-2-222-2-2-2-200000000000000002-22-20000200-22-20000000000000000
χ202222222-2-2222-2-22222-2-2-2-2-2-2220000000022-2-222-2-2-2-20000000000000000-22-220000-2002-220000000000000000
χ212222222-2-2-2-2-222-222222222-22200000000-2-2-2-2-2-222-2-20000000000000000000022-2-20000000000200-200000000
χ222222222-2-2-2-2-222-222222222-22200000000-2-2-2-2-2-222-2-200000000000000000000-2-2220000000000-200200000000
χ23222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-122-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200001-2-21111111000000000000
χ25222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122220000-1-2-2-1-1-11111000000000000
χ26222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000122111-1-1-1-1000000000000
χ27222222-1-2-2222-2-22-1-1-11111-2-2-1-100000000-1-111-1-111113333−3−3−3−33333−3−3−3−32-22-20000-1001-113−33−3000000000000
χ28222222-1-2-2222-2-22-1-1-11111-2-2-1-100000000-1-111-1-111113333−3−3−3−33333−3−3−3−3-22-220000100-11-1−33−33000000000000
χ29222222-1-2-2222-2-22-1-1-11111-2-2-1-100000000-1-111-1-11111−3−3−3−33333−3−3−3−333332-22-20000-1001-11−33−33000000000000
χ30222222-1-2-2222-2-22-1-1-11111-2-2-1-100000000-1-111-1-11111−3−3−3−33333−3−3−3−33333-22-220000100-11-13−33−3000000000000
χ312222-2-22222-2-2-2-22222-2-2-2-22-2-2-2000000002222-2-222-2-200000000000000002-2-220000200-2-220000000000000000
χ322222-2-22222-2-2-2-22222-2-2-2-22-2-2-2000000002222-2-222-2-20000000000000000-222-20000-20022-20000000000000000
χ332222-2-2222-22222-22222222-2-2-2-200000000-2-22222-2-2-2-20000000000000000000022220000000000-200-200000000
χ342222-2-2222-22222-22222222-2-2-2-200000000-2-22222-2-2-2-200000000000000000000-2-2-2-20000000000200200000000
χ352222-2-22-2-2-222-2-2-2222-2-2-2-222-2-200000000-2-2-2-2222222000000000000000000000000000000000002-20-22000000
χ362222-2-22-2-2-222-2-2-2222-2-2-2-222-2-200000000-2-2-2-222222200000000000000000000000000000000000-2202-2000000
χ372222-2-2-1222-2-2-2-22-1-1-111112-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−333332-2-220000-10011-13−3−33000000000000
χ382222-2-2-1222-2-2-2-22-1-1-111112-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−33333-222-20000100-1-11−333−3000000000000
χ392222-2-2-1222-2-2-2-22-1-1-111112-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−32-2-220000-10011-1−333−3000000000000
χ402222-2-2-1222-2-2-2-22-1-1-111112-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−3-222-20000100-1-113−3−33000000000000
χ412222-2-2-1-2-22-2-2222-1-1-1-1-1-1-1-22112222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-11111111122-2-20000-12-2-111-1-111000000000000
χ422222-2-2-1-2-22-2-2222-1-1-1-1-1-1-1-22112222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-111111111-2-22200001-221-1-111-1-1000000000000
χ432222-2-2-1-2-22-2-2222-1-1-1-1-1-1-1-2211-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-122-2-20000-1-22-11111-1-1000000000000
χ442222-2-2-1-2-22-2-2222-1-1-1-1-1-1-1-2211-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-1-2-222000012-21-1-1-1-111000000000000
χ4522-2-20022i−2i02i−2i2-202-2-222-2-2000022−2−2−i2−i2i2i2002i−2i2i−2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200002-22i−2i00000000000000002−2−i2i200
χ4622-2-20022i−2i02i−2i2-202-2-222-2-2000022−2−2−i2−i2i2i2002i−2i2i−2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000-22−2i2i0000000000000000−22i2−i200
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χ4822-2-20022i−2i02i−2i2-202-2-222-2-20000−2−222i2i2−i2−i2002i−2i2i−2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i20000-22−2i2i00000000000000002−2−i2i200
χ4922-2-2002−2i2i0−2i2i2-202-2-222-2-2000022−2−2i2i2−i2−i200−2i2i−2i2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200002-2−2i2i00000000000000002−2i2−i200
χ5022-2-2002−2i2i0−2i2i2-202-2-222-2-2000022−2−2i2i2−i2−i200−2i2i−2i2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000-222i−2i0000000000000000−22−i2i200
χ5122-2-2002−2i2i0−2i2i2-202-2-222-2-20000−2−222−i2−i2i2i200−2i2i−2i2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i200002-2−2i2i0000000000000000−22−i2i200
χ5222-2-2002−2i2i0−2i2i2-202-2-222-2-20000−2−222−i2−i2i2i200−2i2i−2i2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i20000-222i−2i00000000000000002−2i2−i200
χ53444444-244-4-4-4-4-4-4-2-2-22222-44-2-20000000022-2-22222-2-20000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-444-4-2-2-2-2-2-2-24-4-2-200000000222222-2-2220000000000000000000000000000000000000000000000
χ554444-4-4-244-44444-4-2-2-2-2-2-2-2-4-4220000000022-2-2-2-222220000000000000000000000000000000000000000000000
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χ5744-4-40044i−4i0−4i4i-4404-4-4-4-444000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5844-4-4004−4i4i04i−4i-4404-4-4-4-44400000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ5944-4-400-24i−4i04i−4i4-40-222-2-22200002222−22−22−2i2−2i22i22i200−2i2i−2i2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000
χ6044-4-400-24i−4i04i−4i4-40-222-2-2220000−22−2222222i22i2−2i2−2i200−2i2i−2i2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000000000000000000000
χ6144-4-400-24i−4i0−4i4i-440-22222-2-200000000000000−2i2i2i−2i000066−6−6−6−666i6i6−i6−i6−i6−i6i6i6000000000000000000000000000000
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χ6544-4-400-2−4i4i0−4i4i4-40-222-2-22200002222−22−222i22i2−2i2−2i2002i−2i2i−2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000000000000000
χ6644-4-400-2−4i4i0−4i4i4-40-222-2-2220000−22−222222−2i2−2i22i22i2002i−2i2i−2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000
χ674-44-44-4400000000-44-40000004-42i−2i2i−2i2i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ684-44-44-4400000000-44-40000004-4−2i2i−2i2i−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
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χ854-4-4400-20040000-422-2−232323−230000−2i22i22i2−2i20000-22000000−23232ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000
χ864-4-4400-20040000-422-2−232323−2300002i2−2i2−2i22i20000-22000000−2323−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000
χ874-4-4400-200-40000422-223−23−23230000000022−22−22222-2000000−2323000000002ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ884-4-4400-200-40000422-223−23−232300000000−222222−222-2000000−232300000000−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000
χ894-4-4400-200-40000422-2−232323−230000000022−22−22222-200000023−23000000002ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000
χ904-4-4400-200-40000422-2−232323−2300000000−222222−222-200000023−2300000000−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000

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