Finite Group Databasebeta

← Group #14298623

Character table — Group #14298623

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444448888888888888888888888101010101212121220202020202024242424242424243030303040404040404040404040404040406060120120120120
order1244234612124456101010122020202012121520202020303030606060606060606060606060224424444466121210102020202020204444448812121212121224242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1i−ii−i-1-1ii−i−iii−i−i-1-1i−ii−i
χ611111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−ii−ii-1-1−i−iii−i−iii-1-1−ii−ii
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i-1-1ii−i−iii−i−i11−ii−ii
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−ii-1-1−i−iii−i−iii11i−ii−i
χ91111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1
χ101111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111
χ111111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ121111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-1
χ131111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111i−i−ii11ii−i−i−i−iii-1-1i−i−ii
χ141111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−iii−i11−i−iiiii−i−i-1-1−iii−i
χ151111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1i−i−ii11ii−i−i−i−iii11−iii−i
χ161111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−iii−i11−i−iiiii−i−i11i−i−ii
χ1722222-12-1-1-1222-1222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-10000000000002222-1-1-1-1-1-1-1-1-1-1000000
χ1822222-12-1-1-1222-1222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1000000000000-2-2-2-2-1-111111111000000
χ1922222-12-1-1-1222-1222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211110000000000002i−2i2i−2i11−i−iii−i−iii000000
χ2022222-12-1-1-1222-1222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-21111000000000000−2i2i−2i2i11ii−i−iii−i−i000000
χ2122222-12-1-1-1-2-22-1222-1222211-1-2-2-2-2-1-1-1-1-1-1-11111111122220000-2-2-1-1-1-100000000000022-2-211-1-1-1-11111000000
χ2222222-12-1-1-1-2-22-1222-1222211-1-2-2-2-2-1-1-1-1-1-1-11111111122220000-2-2-1-1-1-1000000000000-2-222111111-1-1-1-1000000
χ2322222-12-1-1-1-2-22-1222-1222211-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-200002211110000000000002i−2i−2i2i-1-1−i−iiiii−i−i000000
χ2422222-12-1-1-1-2-22-1222-1222211-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-20000221111000000000000−2i2i2i−2i-1-1ii−i−i−i−iii000000
χ252222-22-22222i−2i2-22-2-2-222-2-22i−2i22i2i−2i−2i2-2-222-2-22i2i2i2i−2i−2i−2i−2i2-2-2200002i−2i-222-200000000000000002i−2i00000000000000
χ262222-22-22222i−2i2-22-2-2-222-2-22i−2i22i2i−2i−2i2-2-222-2-22i2i2i2i−2i−2i−2i−2i-222-20000−2i2i2-2-220000000000000000−2i2i00000000000000
χ272222-22-2222−2i2i2-22-2-2-222-2-2−2i2i2−2i−2i2i2i2-2-222-2-2−2i−2i−2i−2i2i2i2i2i2-2-220000−2i2i-222-20000000000000000−2i2i00000000000000
χ282222-22-2222−2i2i2-22-2-2-222-2-2−2i2i2−2i−2i2i2i2-2-222-2-2−2i−2i−2i−2i2i2i2i2i-222-200002i−2i2-2-2200000000000000002i−2i00000000000000
χ292222-2-1-2-1-1-12i−2i212-2-2122-2-2−ii-12i2i−2i−2i-111-1-111−i−i−i−iiiii2-2-2200002i−2i1-1-110000000000000000−ii−i3i3−i3i33−33−3000000
χ302222-2-1-2-1-1-12i−2i212-2-2122-2-2−ii-12i2i−2i−2i-111-1-111−i−i−i−iiiii2-2-2200002i−2i1-1-110000000000000000−iii3−i3i3−i3−33−33000000
χ312222-2-1-2-1-1-12i−2i212-2-2122-2-2−ii-12i2i−2i−2i-111-1-111−i−i−i−iiiii-222-20000−2i2i-111-10000000000000000i−i3−3−33i3−i3−i3i3000000
χ322222-2-1-2-1-1-12i−2i212-2-2122-2-2−ii-12i2i−2i−2i-111-1-111−i−i−i−iiiii-222-20000−2i2i-111-10000000000000000i−i−333−3−i3i3i3−i3000000
χ332222-2-1-2-1-1-1−2i2i212-2-2122-2-2i−i-1−2i−2i2i2i-111-1-111iiii−i−i−i−i2-2-220000−2i2i1-1-110000000000000000i−i−i3i3−i3i3−33−33000000
χ342222-2-1-2-1-1-1−2i2i212-2-2122-2-2i−i-1−2i−2i2i2i-111-1-111iiii−i−i−i−i2-2-220000−2i2i1-1-110000000000000000i−ii3−i3i3−i33−33−3000000
χ352222-2-1-2-1-1-1−2i2i212-2-2122-2-2i−i-1−2i−2i2i2i-111-1-111iiii−i−i−i−i-222-200002i−2i-111-10000000000000000−ii3−3−33−i3i3i3−i3000000
χ362222-2-1-2-1-1-1−2i2i212-2-2122-2-2i−i-1−2i−2i2i2i-111-1-111iiii−i−i−i−i-222-200002i−2i-111-10000000000000000−ii−333−3i3−i3−i3i3000000
χ3722-2-222-22-2-20022222-2-2-2-2-20020000222-2-2-2-20000000022-2-22-2000022-2-222-2-20000000000000000000000-220000
χ3822-2-222-22-2-20022222-2-2-2-2-20020000222-2-2-2-20000000022-2-2-22000022-2-2-2-22200000000000000000000002-20000
χ3922-2-222-22-2-20022222-2-2-2-2-20020000222-2-2-2-200000000-2-2222-20000-2-22222-2-200000000000000000000002-20000
χ4022-2-222-22-2-20022222-2-2-2-2-20020000222-2-2-2-200000000-2-222-220000-2-222-2-2220000000000000000000000-220000
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χ4322-2-2-2222-2-2002-22-2-22-2-22200200002-2-2-2-22200000000-22-22002i−2i002-22-200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4422-2-2-2222-2-2002-22-2-22-2-22200200002-2-2-2-22200000000-22-2200−2i2i002-22-20000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ45444444444444-14-1-1-14-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100004444000000-1-1-1-1-1-1-1-1000000000000000000000000
χ46444444444444-14-1-1-14-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-4-4-400000011111111000000000000000000000000
χ474444444444-4-4-14-1-1-14-1-1-1-1-4-4-11111-1-1-1-1-1-1-111111111000044-4-4000000-1-1-1-11111000000000000000000000000
χ484444444444-4-4-14-1-1-14-1-1-1-1-4-4-11111-1-1-1-1-1-1-1111111110000-4-4440000001111-1-1-1-1000000000000000000000000
χ494444-44-44444i−4i-1-4-111-4-1-1114i−4i-1−i−iii-111-1-111−i−i−i−iiiii00000000000000−55−55−i5i5−i5i5000000000000000000000000
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χ514444-44-4444−4i4i-1-4-111-4-1-111−4i4i-1ii−i−i-111-1-111iiii−i−i−i−i00000000000000−55−55i5−i5i5−i5000000000000000000000000
χ524444-44-4444−4i4i-1-4-111-4-1-111−4i4i-1ii−i−i-111-1-111iiii−i−i−i−i000000000000005−55−5−i5i5−i5i5000000000000000000000000
χ5344-4-444-44-4-400-14-1-1-1-4111100-1−55−55-1-1-11111−5−555−5−55500004-400000000-1-111−555−5000000000000000000000000
χ5444-4-444-44-4-400-14-1-1-1-4111100-1−55−55-1-1-11111−5−555−5−5550000-440000000011-1-15−5−55000000000000000000000000
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χ5744-4-44-2-4-222004-24442-4-4-4-400-20000-2-2-222220000000044-4-4000000-2-22200000000000000000000000000000000
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χ888-8−8i8i0-4044i−4i00-202−252502i−2i2i5−2i50010000-15−5−ii−i5i5ζ2+ζ11+ζ19−ζ22−ζ31−ζ38+ζ58−ζ59−ζ2−ζ11−ζ19+ζ22+ζ31+ζ38−ζ58+ζ59ζ7−ζ14+ζ23+ζ26+ζ34−ζ43−ζ46−ζ47−ζ7+ζ14−ζ23−ζ26−ζ34+ζ43+ζ46+ζ47ζ2−ζ11−ζ19−ζ22+ζ31−ζ38+ζ58+ζ59−ζ2+ζ11+ζ19+ζ22−ζ31+ζ38−ζ58−ζ59−ζ7−ζ14−ζ23+ζ26+ζ34+ζ43−ζ46+ζ47ζ7+ζ14+ζ23−ζ26−ζ34−ζ43+ζ46−ζ470000000000000000000000000000000000000000000000
χ898-8−8i8i0-4044i−4i00-20225−2502i−2i−2i52i50010000-1−55−iii5−i5−ζ7+ζ14−ζ23−ζ26−ζ34+ζ43+ζ46+ζ47ζ7−ζ14+ζ23+ζ26+ζ34−ζ43−ζ46−ζ47ζ2+ζ11+ζ19−ζ22−ζ31−ζ38+ζ58−ζ59−ζ2−ζ11−ζ19+ζ22+ζ31+ζ38−ζ58+ζ59ζ7+ζ14+ζ23−ζ26−ζ34−ζ43+ζ46−ζ47−ζ7−ζ14−ζ23+ζ26+ζ34+ζ43−ζ46+ζ47ζ2−ζ11−ζ19−ζ22+ζ31−ζ38+ζ58+ζ59−ζ2+ζ11+ζ19+ζ22−ζ31+ζ38−ζ58−ζ590000000000000000000000000000000000000000000000
χ908-8−8i8i0-4044i−4i00-20225−2502i−2i−2i52i50010000-1−55−iii5−i5ζ7−ζ14+ζ23+ζ26+ζ34−ζ43−ζ46−ζ47−ζ7+ζ14−ζ23−ζ26−ζ34+ζ43+ζ46+ζ47−ζ2−ζ11−ζ19+ζ22+ζ31+ζ38−ζ58+ζ59ζ2+ζ11+ζ19−ζ22−ζ31−ζ38+ζ58−ζ59−ζ7−ζ14−ζ23+ζ26+ζ34+ζ43−ζ46+ζ47ζ7+ζ14+ζ23−ζ26−ζ34−ζ43+ζ46−ζ47−ζ2+ζ11+ζ19+ζ22−ζ31+ζ38−ζ58−ζ59ζ2−ζ11−ζ19−ζ22+ζ31−ζ38+ζ58+ζ590000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.