Finite Group Databasebeta

← Group #13160218

Character table — Group #13160218

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1122222222222224444444444444444444444466666666668888888888888888888881212121212121212121212121216161616161616161624242424242424242436363636363672108108144216
order12333334666668833336666121212121224242424242424242424246666666626666666612121212242424242424242481212121224242424242424246666666662666666661616484848482161664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111111-1-11-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-11
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1
χ92222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-222222222220000000002222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000
χ102222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000002222-2-2-2-2-2-2-2-22-2-2-2-22222222200000000000000000000000000000
χ112222222-2222220022222222-2-2-2-2-200000000002-222222222000000000-2-2-2-2000000000-2-2-2-2000000000000000000000000002−222−2−202−200
χ122222222-2222220022222222-2-2-2-2-200000000002-222222222000000000-2-2-2-2000000000-2-2-2-200000000000000000000000000−22−2−2220−2200
χ132222222-2222220022222222-2-2-2-2-20000000000-22-2-2-2-2-2-2-2-2000000000-2-2-2-20000000002222000000000000000000000000002−222−2−20−2200
χ142222222-2222220022222222-2-2-2-2-20000000000-22-2-2-2-2-2-2-2-2000000000-2-2-2-2000000000222200000000000000000000000000−22−2−22202−200
χ15222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-10000000000222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000-1-1-1-1-1-1-1-1-100000000022-1-1-1-1200-10
χ16222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-10000000000222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000-1-1-1-1-1-1-1-1-1000000000-2-21111-20010
χ17222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-10000000000-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1000000000000011111111100000000022-1-1-1-1-20010
χ18222222-12-1222222-1-1-1-1-1-1-1-1-1222222222222-1-10000000000-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000000111111111000000000-2-21111200-10
χ19222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-100000000000
χ20222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-2-2-21111112-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1-2-2-2111111-2-2-211111100000000000
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χ22222-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-2-2-2-2111111-2-2-21111112-1-1-122-1-1-1-1-1-1-2-2111-2-2111111-2-2-2111111222-1-1-1-1-1-100000000000
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χ24222-1-1-12222-1-1-1-2-22-1-1-12-1-1-122-1-1-1-2-2111111-2-22222-1-1-1-1-1-1000i3i3i3−i3−i3−i32-1-1-1-2-2111111-22-1-1-1-2-2111111000i3i3i3−i3−i3−i3000i3i3i3−i3−i3−i300000000000
χ25222-1-1-12222-1-1-1-2-22-1-1-12-1-1-122-1-1-1-2-2111111-2-2-2-2-2-2111111000−i3−i3−i3i3i3i32-1-1-1-2-21111112-211122-1-1-1-1-1-1000−i3−i3−i3i3i3i3000i3i3i3−i3−i3−i300000000000
χ26222-1-1-12222-1-1-1-2-22-1-1-12-1-1-122-1-1-1-2-2111111-2-2-2-2-2-2111111000i3i3i3−i3−i3−i32-1-1-1-2-21111112-211122-1-1-1-1-1-1000i3i3i3−i3−i3−i3000−i3−i3−i3i3i3i300000000000
χ2722-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-12222-1-122-1-1-1-12-1-12-1-12-1-1-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-100000000000
χ2822-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-211-211-211-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-1-211-211-211-211-211-21100000000000
χ2922-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-122-2-211-2-211112-1-12-1-12-1-1-12-1-1-1-122-1-1-1-1-21-21111-2-211112-1-12-1-12-1-1-211-211-21100000000000
χ3022-12-1-1222-12-1-122-12-1-1-12-1-12-12-1-1-1-122-1-1-1-122-2-211-2-21111-211-211-211-12-1-1-1-122-1-1-1-1-21-21111-2-21111-211-211-2112-1-12-1-12-1-100000000000
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χ3222-12-1-1222-12-1-1-2-2-12-1-1-12-1-12-12-1-111-2-21111-2-222-1-122-1-1-1-10i3−i30i3−i30i3−i3-12-1-111-2-21111-2-12-1-111-2-211110i3−i30i3−i30i3−i30i3−i30i3−i30i3−i300000000000
χ3322-12-1-1222-12-1-1-2-2-12-1-1-12-1-12-12-1-111-2-21111-2-2-2-211-2-211110−i3i30−i3i30−i3i3-12-1-111-2-2111121-211-1-122-1-1-1-10−i3i30−i3i30−i3i30i3−i30i3−i30i3−i300000000000
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χ3622-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-12222-1-1-1-122-1-1-2111-2111-2-1-12-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-1-2111-2111-2-2111-2111-200000000000
χ3722-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-122-2-21111-2-2112-1-1-12-1-1-12-1-12-1-1-1-1-122-1-1-211-211111-2-2112-1-1-12-1-1-12-2111-2111-200000000000
χ3822-1-12-1222-1-12-122-1-12-1-1-12-12-1-12-1-1-1-1-122-1-122-2-21111-2-211-2111-2111-2-1-12-1-1-1-1-122-1-1-211-211111-2-211-2111-2111-22-1-1-12-1-1-1200000000000
χ3922-1-12-1222-1-12-1-2-2-1-12-1-1-12-12-1-12-11111-2-211-2-222-1-1-1-122-1-10−i3i3i30−i3−i3i30-1-12-11111-2-211-2-1-12-11111-2-2110−i3i3i30−i3−i3i300−i3i3i30−i3−i3i3000000000000
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χ4222-1-12-1222-1-12-1-2-2-1-12-1-1-12-12-1-12-11111-2-211-2-2-2-21111-2-2110i3−i3−i30i3i3−i30-1-12-11111-2-211211-21-1-1-1-122-1-10i3−i3−i30i3i3−i300−i3i3i30−i3−i3i3000000000000
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χ4522-1-1-12222-1-1-1222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-12222-2-2111111-2-22-1-1-1-12-12-1-1-1-12-1-1-1-1-1-122-2111-2111111-2-22-1-1-1-12-12-1-21111-21-2100000000000
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χ784-4444440-4-4-4-4-422−224444-4-4-4-40000022−2222−2222−2222−2222−220000000000000000000000022−2222−2222−2222−22000000000000000000000000000000000000000000
χ794-4444440-4-4-4-4-4−22224444-4-4-4-400000−2222−2222−2222−2222−222200000000000000000000000−2222−2222−2222−2222000000000000000000000000000000000000000000
χ804-44444-202-4-4-4-422−22-2-2-2-222220000022−2222−2222−2222−22−2200000000000000000000000−22−22−22−22000000000000000000000000000000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000
χ814-44444-202-4-4-4-422−22-2-2-2-222220000022−2222−2222−2222−22−2200000000000000000000000−22−22−22−22000000000000000000000000000000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000
χ824-44444-202-4-4-4-4−2222-2-2-2-2222200000−2222−2222−2222−22222−2000000000000000000000002−22−22−22−2000000000000000000000000000000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000
χ834-44444-202-4-4-4-4−2222-2-2-2-2222200000−2222−2222−2222−22222−2000000000000000000000002−22−22−22−2000000000000000000000000000000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000
χ844-44-2-2-240-4-422222−224-2-2-2-42220000022−22−22−22−2222−220000−2i32i3−2i32i3−2i32i3000000000000022−22−22−22−220000000i6−i6i6−i6i6−i600000000000000000000000000000
χ854-44-2-2-240-4-422222−224-2-2-2-42220000022−22−22−22−2222−2200002i3−2i32i3−2i32i3−2i3000000000000022−22−22−22−220000000−i6i6−i6i6−i6i600000000000000000000000000000
χ864-44-2-2-240-4-4222−22224-2-2-2-422200000−22222−22−22−2−22220000−2i32i3−2i32i3−2i32i30000000000000−22222−22−22−20000000−i6i6−i6i6−i6i600000000000000000000000000000
χ874-44-2-2-240-4-4222−22224-2-2-2-422200000−22222−22−22−2−222200002i3−2i32i3−2i32i3−2i30000000000000−22222−22−22−20000000i6−i6i6−i6i6−i600000000000000000000000000000
χ884-4-24-2-240-42-42222−22-24-2-22-42200000−2222−22−22−2222−2200−2i32i300−2i32i32i3−2i30000000000000−2222−22−22−2200000i6−i600i6−i6−i6i600000000000000000000000000000
χ894-4-24-2-240-42-42222−22-24-2-22-42200000−2222−22−22−2222−22002i3−2i3002i3−2i3−2i32i30000000000000−2222−22−22−2200000−i6i600−i6i6i6−i600000000000000000000000000000
χ904-4-24-2-240-42-422−2222-24-2-22-422000002−2−22222−22−2−222200−2i32i300−2i32i32i3−2i300000000000002−2−22222−22−200000−i6i600−i6i6i6−i600000000000000000000000000000
χ914-4-24-2-240-42-422−2222-24-2-22-422000002−2−22222−22−2−2222002i3−2i3002i3−2i3−2i32i300000000000002−2−22222−22−200000i6−i600i6−i6−i6i600000000000000000000000000000
χ924-4-2-24-240-422-4222−22-2-24-222-4200000−22−2222−22−2222−2200−2i32i32i3−2i300−2i32i30000000000000−22−2222−22−2200000i6−i6−i6i600i6−i600000000000000000000000000000
χ934-4-2-24-240-422-4222−22-2-24-222-4200000−22−2222−22−2222−22002i3−2i3−2i32i3002i3−2i30000000000000−22−2222−22−2200000−i6i6i6−i600−i6i600000000000000000000000000000
χ944-4-2-24-240-422-42−2222-2-24-222-42000002−22−2−22222−2−222200−2i32i32i3−2i300−2i32i300000000000002−22−2−22222−200000−i6i6i6−i600−i6i600000000000000000000000000000
χ954-4-2-24-240-422-42−2222-2-24-222-42000002−22−2−22222−2−2222002i3−2i3−2i32i3002i3−2i300000000000002−22−2−22222−200000i6−i6−i6i600i6−i600000000000000000000000000000
χ964-4-2-2-2440-4222-422−22-2-2-24222-400000−22−22−2222−2222−2200−2i32i3−2i32i32i3−2i3000000000000000−22−22−2222−2200000i6−i6i6−i6−i6i60000000000000000000000000000000
χ974-4-2-2-2440-4222-422−22-2-2-24222-400000−22−22−2222−2222−22002i3−2i32i3−2i3−2i32i3000000000000000−22−22−2222−2200000−i6i6−i6i6i6−i60000000000000000000000000000000
χ984-4-2-2-2440-4222-4−2222-2-2-24222-4000002−22−22−2−2222−222200−2i32i3−2i32i32i3−2i30000000000000002−22−22−2−222200000−i6i6−i6i6i6−i60000000000000000000000000000000
χ994-4-2-2-2440-4222-4−2222-2-2-24222-4000002−22−22−2−2222−2222002i3−2i32i3−2i3−2i32i30000000000000002−22−22−2−222200000i6−i6i6−i6−i6i60000000000000000000000000000000
χ100888-4-4-4-4-8-48-4-4-400-4222-42224-8444000000000000000000000000000004-2-2-200000000000000000000000000000000000000000000000000
χ10188-48-4-4-4-8-4-48-4-4002-4222-42244-84400000000000000000000000000000-24-2-200000000000000000000000000000000000000000000000000
χ10288-4-48-4-4-8-4-4-48-40022-4222-42444-8400000000000000000000000000000-2-24-200000000000000000000000000000000000000000000000000
χ10388-4-4-48-4-8-4-4-4-4800222-4222-44444-800000000000000000000000000000-2-2-2400000000000000000000000000000000000000000000000000
χ1048-88-4-4-4-404-844442−42-42224-2-2-20000042−42−2222−2222−2222−222200000000000000000000000−22222−22−22−2000000000000000000000000000000000000000000
χ1058-88-4-4-4-404-8444−4242-42224-2-2-200000−424222−2222−2222−2222−220000000000000000000000022−22−22−22−22000000000000000000000000000000000000000000
χ1068-8-48-4-4-4044-84442−422-422-24-2-200000−222242−42−2222−2222−2222000000000000000000000002−2−22222−22−2000000000000000000000000000000000000000000
χ1078-8-48-4-4-4044-844−42422-422-24-2-20000022−22−424222−2222−2222−2200000000000000000000000−2222−22−22−22000000000000000000000000000000000000000000
χ1088-8-4-48-4-40444-8442−4222-42-2-24-200000−2222−222242−42−2222−2222000000000000000000000002−22−2−22222−2000000000000000000000000000000000000000000
χ1098-8-4-48-4-40444-84−424222-42-2-24-20000022−2222−22−424222−2222−2200000000000000000000000−22−2222−22−22000000000000000000000000000000000000000000
χ1108-8-4-4-48-404444-842−42222-4-2-2-2400000−2222−2222−222242−42−2222000000000000000000000002−22−22−2−2222000000000000000000000000000000000000000000
χ1118-8-4-4-48-404444-8−4242222-4-2-2-240000022−2222−2222−22−424222−2200000000000000000000000−22−22−2222−22000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.