Finite Group Databasebeta

← Group #10693695

Character table — Group #10693695

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12224444223444444666121212124466888888881212121212128888888888881212242424242424242424242424242424248888888888888824242424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-11iiii−i−i−i−i11-1-11-1ii−i−iii−i−i1111-1-1-1-1ii−i−i1111-1-1-1-1i−iii−i−iii−i−i1-1
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-11iiii−i−i−i−i-1-1111-1ii−i−iii−i−i-1-1-1-11111ii−i−i1111-1-1-1-1−ii−i−iii−i−iii-11
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-11−i−i−i−iiiii11-1-11-1ii−i−iii−i−i1111-1-1-1-1−i−iii-1-1-1-11111i−iii−i−i−i−iii-11
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-11−i−i−i−iiiii-1-1111-1ii−i−iii−i−i-1-1-1-11111−i−iii-1-1-1-11111−ii−i−iiiii−i−i1-1
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1−i−iii−i−iii111-1-11iiii−i−i−i−i11-1-11-1−i−iii−i−iii1111-1-1-1-1ii−i−i-1-1-1-11111−ii−i−iiiii−i−i-11
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1−i−iii−i−iii111-1-11iiii−i−i−i−i-1-1111-1−i−iii−i−iii-1-1-1-11111ii−i−i-1-1-1-11111i−iii−i−i−i−iii1-1
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1−i−iii−i−iii111-1-11−i−i−i−iiiii11-1-11-1−i−iii−i−iii1111-1-1-1-1−i−iii1111-1-1-1-1−ii−i−iii−i−iii1-1
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1−i−iii−i−iii111-1-11−i−i−i−iiiii-1-1111-1−i−iii−i−iii-1-1-1-11111−i−iii1111-1-1-1-1i−iii−i−iii−i−i-11
χ172222222222222-2-2-2-22222222-2-2222222-2-2-2-22-2-2-2-22000000000000-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-222-2-2-2-222222-2-2-2-22000000000000-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ232222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-12222-2-2-2-2-11111-100000000000011-1-1-1-11111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ242222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-12222-2-2-2-2-11111-100000000000011-1-1-1-11111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ252222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-2-2-2-22222-11111-1000000000000111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ262222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-2-2-2-22222-11111-1000000000000111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ2722222222-2-22-2-222222222222-2-2-2-200000000-22222-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ2822222222-2-22-2-222222222222-2-2-2-200000000-22222-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ2922222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-2-2-2-2-200000000000022000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ3022222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-2-2-2-2-20000000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-2-222200000000-222-2-2-22i2i2i2i−2i−2i−2i−2i0000-220000000000000000−2i−2i2i2i00000000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-2-222200000000-222-2-2-2−2i−2i−2i−2i2i2i2i2i0000-2200000000000000002i2i−2i−2i00000000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-22200000000-2-2-222-20000000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-22200000000-2-2-222-20000000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ352222-2-2-2-2-2-2222-2-222222-2-2-2-2-22-2-22i2i−2i−2i−2i−2i2i2i2-2-2222000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ362222-2-2-2-2-2-2222-2-222222-2-2-2-2-22-2-2−2i−2i2i2i2i2i−2i−2i2-2-2222000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-2-1-1-111112-2112i2i−2i−2i2i2i−2i−2i-1-1-111-10000000022-2-2-11−i−iii−i−iii-1-1-1-111110000000000002i−2i−i−iii000000
χ382222-2-2-2-2-2-2-12222-2-2-1-1-111112-2112i2i−2i−2i2i2i−2i−2i-1-1-111-100000000-2-222-11−i−iii−i−iii1111-1-1-1-1000000000000−2i2iii−i−i000000
χ392222-2-2-2-2-2-2-12222-2-2-1-1-111112-211−2i−2i2i2i−2i−2i2i2i-1-1-111-10000000022-2-2-11ii−i−iii−i−i-1-1-1-11111000000000000−2i2iii−i−i000000
χ402222-2-2-2-2-2-2-12222-2-2-1-1-111112-211−2i−2i2i2i−2i−2i2i2i-1-1-111-100000000-2-222-11ii−i−iii−i−i1111-1-1-1-10000000000002i−2i−i−iii000000
χ412222-2-2-2-2-2-2-122-2-222-1-1-11111-22112i2i−2i−2i−2i−2i2i2i-111-1-1-10000000000001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000000000003−3−33000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-11111-22112i2i−2i−2i−2i−2i2i2i-111-1-1-10000000000001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000000−333−3000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i-111-1-1-10000000000001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000000−333−3000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i-111-1-1-10000000000001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000000000003−3−33000000
χ4522-2-222-2-22-222-200002-2-222-2-2002-22-22-2000020000-222−2−222−2−20000002-22-20000000000002−22−22−22−22−22−2000000000000
χ4622-2-222-2-22-222-200002-2-222-2-2002-22-22-2000020000-2−2−222−2−2220000002-22-2000000000000−22−22−22−22−22−22000000000000
χ4722-2-222-2-22-222-200002-2-222-2-2002-2-22-22000020000-222−2−222−2−2000000-22-220000000000002−22−2−22−22−22−22000000000000
χ4822-2-222-2-22-222-200002-2-222-2-2002-2-22-22000020000-2−2−222−2−222000000-22-22000000000000−22−222−22−22−22−2000000000000
χ4922-2-222-2-2-222-2200002-2-222-2-200-2200002i−2i2i−2i-20000222−2−222−2−200000000002i−2i2i−2i00000000−22−22−i2i2i2−i2−i2i2i2−i2000000000000
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χ5122-2-222-2-2-222-2200002-2-222-2-200-220000−2i2i−2i2i-20000222−2−222−2−20000000000−2i2i−2i2i00000000−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ5222-2-222-2-2-222-2200002-2-222-2-200-220000−2i2i−2i2i-200002−2−222−2−2220000000000−2i2i−2i2i000000002−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ5322-2-2-2-2222-22-2200002-2-2-2-222002-200002-2-22-200002−i2−i2i2i2i2i2−i2−i200000000002-2-2200000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ5422-2-2-2-2222-22-2200002-2-2-2-222002-200002-2-22-200002i2i2−i2−i2−i2−i2i2i200000000002-2-2200000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ5522-2-2-2-2222-22-2200002-2-2-2-222002-20000-222-2-200002−i2−i2i2i2i2i2−i2−i20000000000-222-200000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
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χ5722-2-2-2-222-2222-200002-2-2-2-22200-222i−2i−2i2i000020000-2−i2−i2i2i2i2i2−i2−i20000002i−2i−2i2i000000000000−i2i2i2−i2−22−222−22−2000000000000
χ5822-2-2-2-222-2222-200002-2-2-2-22200-222i−2i−2i2i000020000-2i2i2−i2−i2−i2−i2i2i20000002i−2i−2i2i000000000000i2−i2−i2i22−22−2−22−22000000000000
χ5922-2-2-2-222-2222-200002-2-2-2-22200-22−2i2i2i−2i000020000-2−i2−i2i2i2i2i2−i2−i2000000−2i2i2i−2i000000000000−i2i2i2−i22−22−2−22−22000000000000
χ6022-2-2-2-222-2222-200002-2-2-2-22200-22−2i2i2i−2i000020000-2i2i2−i2−i2−i2−i2i2i2000000−2i2i2i−2i000000000000i2−i2−i2i2−22−222−22−2000000000000
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χ6944444444-4-4-2-4-44444-2-2-2-2-2-2-2-4-422000000002-2-2-2-22000000000000220000000000000000000000000000000000000000
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χ914-4-444i−4i−4i4i004000000-4-444i−4i−4i4i0000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000000000
χ924-4-444i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i0000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000000000
χ944-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000000000
χ958-8-888i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

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