Finite Group Databasebeta

← Group #13160234

Character table — Group #13160234

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1122222222222224444444444444444444444466666666668888888888888888888881212121212121212121212121216161616161616161624242424242424242436363636363672108108144216
order123333346666688333366661212121212242424242424242424242412121212121212124121212121212121212121212242424242424242466668242424242424242412121212121212121226666666616164848484841616124
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
χ92222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-222222222220000000002222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-200000000000000000000000000000
χ102222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000002222-2-2-2-2-2-2-2-2-2-2-2-222222222200000000000000000000000000000
χ112222222-2222220022222222-2-2-2-2-200000000002-2-2-2-2-2-2-2-2-2000000000-2-2-2-20000000022220000000000000000000000000002−222−2−202−200
χ122222222-2222220022222222-2-2-2-2-200000000002-2-2-2-2-2-2-2-2-2000000000-2-2-2-2000000002222000000000000000000000000000−22−2−2220−2200
χ132222222-2222220022222222-2-2-2-2-20000000000-2222222222000000000-2-2-2-200000000-2-2-2-20000000000000000000000000002−222−2−20−2200
χ142222222-2222220022222222-2-2-2-2-20000000000-2222222222000000000-2-2-2-200000000-2-2-2-2000000000000000000000000000−22−2−22202−200
χ152222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-100000000000
χ162222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-2-2-21111112-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-2111111-2-2-211111100000000000
χ172222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-2-2-2-2111111222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-2111-2-2-2111111222-1-1-1-1-1-1-2-2-211111100000000000
χ182222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-2-2-2-2111111-2-2-21111112-1-1-122-1-1-1-1-1-1-2111-2-2-2111111-2-2-2111111222-1-1-1-1-1-100000000000
χ192222-1-1-122-1-1-12-2-22-1-1-12-1-1-122-1-1-1-2-2111111-2-22222-1-1-1-1-1-1000−i3−i3−i3i3i3i32-1-1-1-2-21111112-1-1-1-2-2-2111111000−i3−i3−i3i3i3i3000−i3−i3−i3i3i3i300000000000
χ202222-1-1-122-1-1-12-2-22-1-1-12-1-1-122-1-1-1-2-2111111-2-22222-1-1-1-1-1-1000i3i3i3−i3−i3−i32-1-1-1-2-21111112-1-1-1-2-2-2111111000i3i3i3−i3−i3−i3000i3i3i3−i3−i3−i300000000000
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χ23222-12-1-12-12-1-1222-12-1-1-12-1-12-12-1-1-1-122-1-1-1-12222-1-122-1-1-1-12-1-12-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-12-1-122-1-1-1-12-1-12-1-12-1-12-1-12-1-12-1-100000000000
χ24222-12-1-12-12-1-1222-12-1-1-12-1-12-12-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-211-211-211-12-1-1-1-122-1-1-1-1-12-1-12-1-122-1-1-1-1-211-211-211-211-211-21100000000000
χ25222-12-1-12-12-1-1222-12-1-1-12-1-12-12-1-1-1-122-1-1-1-122-2-211-2-211112-1-12-1-12-1-1-12-1-1-1-122-1-1-1-11-211-211-2-211112-1-12-1-12-1-1-211-211-21100000000000
χ26222-12-1-12-12-1-1222-12-1-1-12-1-12-12-1-1-1-122-1-1-1-122-2-211-2-21111-211-211-211-12-1-1-1-122-1-1-1-11-211-211-2-21111-211-211-2112-1-12-1-12-1-100000000000
χ27222-12-1-12-12-1-12-2-2-12-1-1-12-1-12-12-1-111-2-21111-2-222-1-122-1-1-1-10−i3i30−i3i30−i3i3-12-1-111-2-21111-12-1-1-211-2-211110−i3i30−i3i30−i3i30−i3i30−i3i30−i3i300000000000
χ28222-12-1-12-12-1-12-2-2-12-1-1-12-1-12-12-1-111-2-21111-2-222-1-122-1-1-1-10i3−i30i3−i30i3−i3-12-1-111-2-21111-12-1-1-211-2-211110i3−i30i3−i30i3−i30i3−i30i3−i30i3−i300000000000
χ29222-12-1-12-12-1-12-2-2-12-1-1-12-1-12-12-1-111-2-21111-2-2-2-211-2-211110−i3i30−i3i30−i3i3-12-1-111-2-211111-2112-1-122-1-1-1-10−i3i30−i3i30−i3i30i3−i30i3−i30i3−i300000000000
χ30222-12-1-12-12-1-12-2-2-12-1-1-12-1-12-12-1-111-2-21111-2-2-2-211-2-211110i3−i30i3−i30i3−i3-12-1-111-2-211111-2112-1-122-1-1-1-10i3−i30i3−i30i3−i30−i3i30−i3i30−i3i300000000000
χ31222-1-12-12-1-12-1222-1-12-1-1-12-12-1-12-1-1-1-1-122-1-12222-1-1-1-122-1-12-1-1-12-1-1-12-1-12-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-12-1-1-12-1-1-122-1-1-12-1-1-1200000000000
χ32222-1-12-12-1-12-1222-1-12-1-1-12-12-1-12-1-1-1-1-122-1-12222-1-1-1-122-1-1-2111-2111-2-1-12-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-2111-2111-2-2111-2111-200000000000
χ33222-1-12-12-1-12-1222-1-12-1-1-12-12-1-12-1-1-1-1-122-1-122-2-21111-2-2112-1-1-12-1-1-12-1-12-1-1-1-1-122-1-111-21-21111-2-2112-1-1-12-1-1-12-2111-2111-200000000000
χ34222-1-12-12-1-12-1222-1-12-1-1-12-12-1-12-1-1-1-1-122-1-122-2-21111-2-211-2111-2111-2-1-12-1-1-1-1-122-1-111-21-21111-2-211-2111-2111-22-1-1-12-1-1-1200000000000
χ35222-1-12-12-1-12-12-2-2-1-12-1-1-12-12-1-12-11111-2-211-2-222-1-1-1-122-1-10−i3i3i30−i3−i3i30-1-12-11111-2-211-1-12-1-21111-2-2110−i3i3i30−i3−i3i300−i3i3i30−i3−i3i3000000000000
χ36222-1-12-12-1-12-12-2-2-1-12-1-1-12-12-1-12-11111-2-211-2-222-1-1-1-122-1-10i3−i3−i30i3i3−i30-1-12-11111-2-211-1-12-1-21111-2-2110i3−i3−i30i3i3−i300i3−i3−i30i3i3−i3000000000000
χ37222-1-12-12-1-12-12-2-2-1-12-1-1-12-12-1-12-11111-2-211-2-2-2-21111-2-2110−i3i3i30−i3−i3i30-1-12-11111-2-21111-212-1-1-1-122-1-10−i3i3i30−i3−i3i300i3−i3−i30i3i3−i3000000000000
χ38222-1-12-12-1-12-12-2-2-1-12-1-1-12-12-1-12-11111-2-211-2-2-2-21111-2-2110i3−i3−i30i3i3−i30-1-12-11111-2-21111-212-1-1-1-122-1-10i3−i3−i30i3i3−i300−i3i3i30−i3−i3i3000000000000
χ39222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-1222222-1-1-1-1-1-1222-1-1-1-12-12-1-1-1-12-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-1-12-12-12-1-1-1-12-12-100000000000
χ40222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-1222222-1-1-1-1-1-122-21111-21-21-1-1-12-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-21111-21-21-21111-21-2100000000000
χ41222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-12222-2-2111111-2-22-1-1-1-12-12-1-1-1-12-1-1-1-1-1-122111-2-2111111-2-22-1-1-1-12-12-1-21111-21-2100000000000
χ42222-1-1-122-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-1-1-1-12222-2-2111111-2-2-21111-21-21-1-1-12-1-1-1-1-1-122111-2-2111111-2-2-21111-21-212-1-1-1-12-12-100000000000
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χ44222-1-1-122-1-1-122-2-2-1-1-12-1-1-122-1-1-12111111-2-2-2-222-1-1-1-1-1-1220i3−i3i3−i30−i30i3-1-1-12111111-2-2-1-1-12-2111111-2-20i3−i3i3−i30−i30i30i3−i3i3−i30−i30i300000000000
χ45222-1-1-122-1-1-122-2-2-1-1-12-1-1-122-1-1-12111111-2-2-2-2-2-2111111-2-20−i3i3−i3i30i30−i3-1-1-12111111-2-2111-22-1-1-1-1-1-1220−i3i3−i3i30i30−i30i3−i3i3−i30−i30i300000000000
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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
χ804-444-2-2-20-4222-422−224-2-2-2-42220000022−22−22−22−2222−22000023−2323−2323−23000000000000022−22−22−22−2200000006−66−66−600000000000000000000000000000
χ814-444-2-2-20-4222-422−224-2-2-2-42220000022−22−22−22−2222−220000−2323−2323−2323000000000000022−22−22−22−220000000−66−66−6600000000000000000000000000000
χ824-444-2-2-20-4222-4−22224-2-2-2-422200000−22222−22−22−2−2222000023−2323−2323−230000000000000−22222−22−22−20000000−66−66−6600000000000000000000000000000
χ834-444-2-2-20-4222-4−22224-2-2-2-422200000−22222−22−22−2−22220000−2323−2323−23230000000000000−22222−22−22−200000006−66−66−600000000000000000000000000000
χ844-44-24-2-202-422-422−22-24-2-22-42200000−2222−22−22−2222−220023−230023−23−23230000000000000−2222−22−22−22000006−6006−6−6600000000000000000000000000000
χ854-44-24-2-202-422-422−22-24-2-22-42200000−2222−22−22−2222−2200−232300−232323−230000000000000−2222−22−22−2200000−6600−666−600000000000000000000000000000
χ864-44-24-2-202-422-4−2222-24-2-22-422000002−2−22222−22−2−22220023−230023−23−232300000000000002−2−22222−22−200000−6600−666−600000000000000000000000000000
χ874-44-24-2-202-422-4−2222-24-2-22-422000002−2−22222−22−2−222200−232300−232323−2300000000000002−2−22222−22−2000006−6006−6−6600000000000000000000000000000
χ884-44-2-24-2022-42-422−22-2-24-222-4200000−22−2222−22−2222−220023−23−23230023−230000000000000−22−2222−22−22000006−6−66006−600000000000000000000000000000
χ894-44-2-24-2022-42-422−22-2-24-222-4200000−22−2222−22−2222−2200−232323−2300−23230000000000000−22−2222−22−2200000−666−600−6600000000000000000000000000000
χ904-44-2-24-2022-42-4−2222-2-24-222-42000002−22−2−22222−2−22220023−23−23230023−2300000000000002−22−2−22222−200000−666−600−6600000000000000000000000000000
χ914-44-2-24-2022-42-4−2222-2-24-222-42000002−22−2−22222−2−222200−232323−2300−232300000000000002−22−2−22222−2000006−6−66006−600000000000000000000000000000
χ924-44-2-2-240222-4-422−22-2-2-24222-400000−22−22−2222−2222−220023−2323−23−2323000000000000000−22−22−2222−22000006−66−6−660000000000000000000000000000000
χ934-44-2-2-240222-4-422−22-2-2-24222-400000−22−22−2222−2222−2200−2323−232323−23000000000000000−22−22−2222−2200000−66−666−60000000000000000000000000000000
χ944-44-2-2-240222-4-4−2222-2-2-24222-4000002−22−22−2−2222−22220023−2323−23−23230000000000000002−22−22−2−222200000−66−666−60000000000000000000000000000000
χ954-44-2-2-240222-4-4−2222-2-2-24222-4000002−22−22−2−2222−222200−2323−232323−230000000000000002−22−22−2−2222000006−66−6−660000000000000000000000000000000
χ964-4-244440-4-4-4-4222−22-2-2-2-222220000022−2222−2222−2222−22−2200000000000000000000000−22−22−22−22000000000000000000000000000000000−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ4700000
χ974-4-244440-4-4-4-4222−22-2-2-2-222220000022−2222−2222−2222−22−2200000000000000000000000−22−22−22−22000000000000000000000000000000000ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ4700000
χ984-4-244440-4-4-4-42−2222-2-2-2-2222200000−2222−2222−2222−22222−2000000000000000000000002−22−22−22−2000000000000000000000000000000000−ζ25+ζ31+ζ41−ζ47ζ25−ζ31−ζ41+ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ4300000
χ994-4-244440-4-4-4-42−2222-2-2-2-2222200000−2222−2222−2222−22222−2000000000000000000000002−22−22−22−2000000000000000000000000000000000ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ4300000
χ10088-48-4-4-4-88-4-4-4-400-4222-42224-8444000000000000000000000000000004-2-2-200000000000000000000000000000000000000000000000000
χ10188-4-48-4-4-8-48-4-4-4002-4222-42244-84400000000000000000000000000000-24-2-200000000000000000000000000000000000000000000000000
χ10288-4-4-48-4-8-4-48-4-40022-4222-42444-8400000000000000000000000000000-2-24-200000000000000000000000000000000000000000000000000
χ10388-4-4-4-48-8-4-4-48-400222-4222-44444-800000000000000000000000000000-2-2-2400000000000000000000000000000000000000000000000000
χ1048-8-48-4-4-40-8444442−42-42224-2-2-20000042−42−2222−2222−2222−222200000000000000000000000−22222−22−22−2000000000000000000000000000000000000000000
χ1058-8-48-4-4-40-84444−4242-42224-2-2-200000−424222−2222−2222−2222−220000000000000000000000022−22−22−22−22000000000000000000000000000000000000000000
χ1068-8-4-48-4-404-844442−422-422-24-2-200000−222242−42−2222−2222−2222000000000000000000000002−2−22222−22−2000000000000000000000000000000000000000000
χ1078-8-4-48-4-404-8444−42422-422-24-2-20000022−22−424222−2222−2222−2200000000000000000000000−2222−22−22−22000000000000000000000000000000000000000000
χ1088-8-4-4-48-4044-84442−4222-42-2-24-200000−2222−222242−42−2222−2222000000000000000000000002−22−2−22222−2000000000000000000000000000000000000000000
χ1098-8-4-4-48-4044-844−424222-42-2-24-20000022−2222−22−424222−2222−2200000000000000000000000−22−2222−22−22000000000000000000000000000000000000000000
χ1108-8-4-4-4-480444-8442−42222-4-2-2-2400000−2222−2222−222242−42−2222000000000000000000000002−22−22−2−2222000000000000000000000000000000000000000000
χ1118-8-4-4-4-480444-84−4242222-4-2-2-240000022−2222−2222−22−424222−2200000000000000000000000−22−22−2222−22000000000000000000000000000000000000000000

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