Finite Group Databasebeta

← Group #14512476

Character table — Group #14512476

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122333344444444555566888888881010121212121212121215151515161616161616161616161616161616163030404040404040404060606060606060606060606060606060
order12224422225101010202020204444443666121212124410101010202020204444151530303030303060606060606060604412121212121212128888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111111111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ4111111111111111111-1-1-1-11111111111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ51111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ61111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ71111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ81111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ91-11-1i−i11-1-111-1-1ii−i−i11-1-1i−i1-11-1ii−i−ii−i11-1-1ii−i−i11-1-11111-1-1-1-1iiii−i−i−i−ii−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ101-11-1i−i11-1-111-1-1ii−i−i11-1-1i−i1-11-1ii−i−ii−i11-1-1ii−i−i11-1-11111-1-1-1-1iiii−i−i−i−ii−i11-1-1ii−i−i-11−ii-11−ii-11−ii-11−ii
χ111-11-1i−i11-1-111-1-1ii−i−i-1-111i−i1-11-1ii−i−i−ii11-1-1ii−i−i-1-1111111-1-1-1-1iiii−i−i−i−i−ii-1-111−i−iiii−i-11−ii1-1i−i-11−ii1-1
χ121-11-1i−i11-1-111-1-1ii−i−i-1-111i−i1-11-1ii−i−i−ii11-1-1ii−i−i-1-1111111-1-1-1-1iiii−i−i−i−i−ii-1-111−i−iii−ii1-1i−i-11−ii1-1i−i-11
χ131-11-1−ii11-1-111-1-1−i−iii11-1-1−ii1-11-1−i−iii−ii11-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−ii11-1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii
χ141-11-1−ii11-1-111-1-1−i−iii11-1-1−ii1-11-1−i−iii−ii11-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−ii11-1-1−i−iii-11i−i-11i−i-11i−i-11i−i
χ151-11-1−ii11-1-111-1-1−i−iii-1-111−ii1-11-1−i−iiii−i11-1-1−i−iii-1-1111111-1-1-1-1−i−i−i−iiiiii−i-1-111ii−i−ii−i1-1−ii-11i−i1-1−ii-11
χ161-11-1−ii11-1-111-1-1−i−iii-1-111−ii1-11-1−i−iiii−i11-1-1−i−iii-1-1111111-1-1-1-1−i−i−i−iiiiii−i-1-111ii−i−i−ii-11i−i1-1−ii-11i−i1-1
χ17222222222222222222222222-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ18222222222222222222-2-2-2-222-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111110000000000000000
χ192222-2-222222222-2-2-2-22222-2-2-1-1-1-11111-2-22222-2-2-2-22222-1-1-1-1-1-1-1-111111111-2-2-1-1-1-111110000000000000000
χ202222-2-222222222-2-2-2-2-2-2-2-2-2-2-1-1-1-11111222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111221111-1-1-1-10000000000000000
χ2122-2-2002-22-22-2-2200002i−2i2i−2i0022-2-20000002-22-200002i−2i2i−2i22-2-2-2-22200000000002i−2i2i−2i00000000000000000000
χ2222-2-2002-22-22-2-2200002i−2i2i−2i00-1-111−i3i3−i3i3002-22-200002i−2i2i−2i-1-11111-1-1−i3−i3i3i3−i3−i3i3i300−ii−ii3−33−30000000000000000
χ2322-2-2002-22-22-2-2200002i−2i2i−2i00-1-111i3−i3i3−i3002-22-200002i−2i2i−2i-1-11111-1-1i3i3−i3−i3i3i3−i3−i300−ii−ii−33−330000000000000000
χ2422-2-2002-22-22-2-220000−2i2i−2i2i0022-2-20000002-22-20000−2i2i−2i2i22-2-2-2-2220000000000−2i2i−2i2i00000000000000000000
χ2522-2-2002-22-22-2-220000−2i2i−2i2i00-1-111−i3i3−i3i3002-22-20000−2i2i−2i2i-1-11111-1-1−i3−i3i3i3−i3−i3i3i300i−ii−i−33−330000000000000000
χ2622-2-2002-22-22-2-220000−2i2i−2i2i00-1-111i3−i3i3−i3002-22-20000−2i2i−2i2i-1-11111-1-1i3i3−i3−i3i3i3−i3−i300i−ii−i3−33−30000000000000000
χ272-22-22i−2i22-2-222-2-22i2i−2i−2i22-2-22i−2i-11-11−i−iii2i−2i22-2-22i2i−2i−2i22-2-2-1-1-1-11111−i−i−i−iiiii2i−2i-1-111−i−iii0000000000000000
χ282-22-22i−2i22-2-222-2-22i2i−2i−2i-2-2222i−2i-11-11−i−iii−2i2i22-2-22i2i−2i−2i-2-222-1-1-1-11111−i−i−i−iiiii−2i2i11-1-1ii−i−i0000000000000000
χ292-22-2−2i2i22-2-222-2-2−2i−2i2i2i22-2-2−2i2i-11-11ii−i−i−2i2i22-2-2−2i−2i2i2i22-2-2-1-1-1-11111iiii−i−i−i−i−2i2i-1-111ii−i−i0000000000000000
χ302-22-2−2i2i22-2-222-2-2−2i−2i2i2i-2-222−2i2i-11-11ii−i−i2i−2i22-2-2−2i−2i2i2i-2-222-1-1-1-11111iiii−i−i−i−i2i−2i11-1-1−i−iii0000000000000000
χ312-2-22002-2-222-22-200002i−2i−2i2i002-2-220000002-2-2200002i−2i−2i2i22-2-222-2-200000000002i−2i−2i2i00000000000000000000
χ322-2-22002-2-222-22-200002i−2i−2i2i00-111-13−3−33002-2-2200002i−2i−2i2i-1-111-1-11133−3−3−3−33300−iii−ii3−i3−i3i30000000000000000
χ332-2-22002-2-222-22-200002i−2i−2i2i00-111-1−333−3002-2-2200002i−2i−2i2i-1-111-1-111−3−33333−3−300−iii−i−i3i3i3−i30000000000000000
χ342-2-22002-2-222-22-20000−2i2i2i−2i002-2-220000002-2-220000−2i2i2i−2i22-2-222-2-20000000000−2i2i2i−2i00000000000000000000
χ352-2-22002-2-222-22-20000−2i2i2i−2i00-111-13−3−33002-2-220000−2i2i2i−2i-1-111-1-11133−3−3−3−33300i−i−ii−i3i3i3−i30000000000000000
χ362-2-22002-2-222-22-20000−2i2i2i−2i00-111-1−333−3002-2-220000−2i2i2i−2i-1-111-1-111−3−33333−3−300i−i−iii3−i3−i3i30000000000000000
χ37333333-1-1-1-1333333333333-1-10000000033-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-10000000011111111-1-1-1-1-1-1-1-1
χ38333333-1-1-1-1333333333333-1-10000000033-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-100000000-1-1-1-1-1-1-1-111111111
χ39333333-1-1-1-133333333-3-3-3-3-1-100000000-3-3-1-1-1-1-1-1-1-1111100000000000000001100000000iiii−i−i−i−i−i−i−i−iiiii
χ40333333-1-1-1-133333333-3-3-3-3-1-100000000-3-3-1-1-1-1-1-1-1-1111100000000000000001100000000−i−i−i−iiiiiiiii−i−i−i−i
χ413333-3-3-1-1-1-13333-3-3-3-333331100000000-3-3-1-1-1-11111-1-1-1-10000000000000000110000000011-1-111-1-1-1-111-1-111
χ423333-3-3-1-1-1-13333-3-3-3-333331100000000-3-3-1-1-1-11111-1-1-1-100000000000000001100000000-1-111-1-11111-1-111-1-1
χ433333-3-3-1-1-1-13333-3-3-3-3-3-3-3-3110000000033-1-1-1-1111111110000000000000000-1-100000000ii−i−i−i−iii−i−iiiii−i−i
χ443333-3-3-1-1-1-13333-3-3-3-3-3-3-3-3110000000033-1-1-1-1111111110000000000000000-1-100000000−i−iiiii−i−iii−i−i−i−iii
χ453-33-33i−3i-1-11133-3-33i3i−3i−3i33-3-3−ii000000003i−3i-1-111−i−iii-1-1110000000000000000−ii000000001-1i−i1-1i−i-11−ii-11−ii
χ463-33-33i−3i-1-11133-3-33i3i−3i−3i33-3-3−ii000000003i−3i-1-111−i−iii-1-1110000000000000000−ii00000000-11−ii-11−ii1-1i−i1-1i−i
χ473-33-33i−3i-1-11133-3-33i3i−3i−3i-3-333−ii00000000−3i3i-1-111−i−iii11-1-10000000000000000i−i00000000i−i-11−ii1-1−ii1-1i−i-11
χ483-33-33i−3i-1-11133-3-33i3i−3i−3i-3-333−ii00000000−3i3i-1-111−i−iii11-1-10000000000000000i−i00000000−ii1-1i−i-11i−i-11−ii1-1
χ493-33-3−3i3i-1-11133-3-3−3i−3i3i3i33-3-3i−i00000000−3i3i-1-111ii−i−i-1-1110000000000000000i−i000000001-1−ii1-1−ii-11i−i-11i−i
χ503-33-3−3i3i-1-11133-3-3−3i−3i3i3i33-3-3i−i00000000−3i3i-1-111ii−i−i-1-1110000000000000000i−i00000000-11i−i-11i−i1-1−ii1-1−ii
χ513-33-3−3i3i-1-11133-3-3−3i−3i3i3i-3-333i−i000000003i−3i-1-111ii−i−i11-1-10000000000000000−ii00000000i−i1-1−ii-11−ii-11i−i1-1
χ523-33-3−3i3i-1-11133-3-3−3i−3i3i3i-3-333i−i000000003i−3i-1-111ii−i−i11-1-10000000000000000−ii00000000−ii-11i−i1-1i−i1-1−ii-11
χ534444444444-1-1-1-1-1-1-1-10000444444444400-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ544444444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-200-1-1-1-1-1-1-1-100001−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ554444444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-200-1-1-1-1-1-1-1-100001+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ564444-4-44444-1-1-1-111110000-4-44444-4-4-4-400-1-1-1-111110000-1-1-1-1-1-1-1-11111111100000000000000000000000000
χ574444-4-44444-1-1-1-111110000-4-4-2-2-2-2222200-1-1-1-1111100001−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ584444-4-44444-1-1-1-111110000-4-4-2-2-2-2222200-1-1-1-1111100001+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ5944-4-4004-44-4-111-1−55−5500000044-4-4000000-11-11−55−550000-1-11111-1-1−555−5−555−500000000000000000000000000
χ6044-4-4004-44-4-111-1−55−55000000-2-222−2i32i3−2i32i300-11-11−55−5500001+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ5800000000000000000000000000
χ6144-4-4004-44-4-111-1−55−55000000-2-2222i3−2i32i3−2i300-11-11−55−5500001−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ4600000000000000000000000000
χ6244-4-4004-44-4-111-15−55−500000044-4-4000000-11-115−55−50000-1-11111-1-15−5−555−5−5500000000000000000000000000
χ6344-4-4004-44-4-111-15−55−5000000-2-222−2i32i3−2i32i300-11-115−55−500001−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ46ζ14−ζ22+ζ26−ζ58ζ2−ζ34+ζ38−ζ46−ζ14+ζ22−ζ26+ζ58−ζ2+ζ34−ζ38+ζ4600000000000000000000000000
χ6444-4-4004-44-4-111-15−55−5000000-2-2222i3−2i32i3−2i300-11-115−55−500001+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ58−ζ2+ζ34−ζ38+ζ46−ζ14+ζ22−ζ26+ζ58ζ2−ζ34+ζ38−ζ46ζ14−ζ22+ζ26−ζ5800000000000000000000000000
χ654-44-44i−4i44-4-4-1-111−i−iii00004i−4i4-44-44i4i−4i−4i00-1-111−i−iii0000-1-1-1-11111−i−i−i−iiiii00000000000000000000000000
χ664-44-44i−4i44-4-4-1-111−i−iii00004i−4i-22-22−2i−2i2i2i00-1-111−i−iii00001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ4700000000000000000000000000
χ674-44-44i−4i44-4-4-1-111−i−iii00004i−4i-22-22−2i−2i2i2i00-1-111−i−iii00001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ5900000000000000000000000000
χ684-44-4−4i4i44-4-4-1-111ii−i−i0000−4i4i4-44-4−4i−4i4i4i00-1-111ii−i−i0000-1-1-1-11111iiii−i−i−i−i00000000000000000000000000
χ694-44-4−4i4i44-4-4-1-111ii−i−i0000−4i4i-22-222i2i−2i−2i00-1-111ii−i−i00001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ4700000000000000000000000000
χ704-44-4−4i4i44-4-4-1-111ii−i−i0000−4i4i-22-222i2i−2i−2i00-1-111ii−i−i00001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59−ζ19−ζ23−ζ31−ζ47−ζ7−ζ11−ζ43−ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ59ζ19+ζ23+ζ31+ζ47ζ7+ζ11+ζ43+ζ5900000000000000000000000000
χ714-4-44004-4-44-11-11−i5i5i5−i50000004-4-44000000-111-1−i5i5i5−i50000-1-111-1-111−i5i5i5−i5i5−i5−i5i500000000000000000000000000
χ724-4-44004-4-44-11-11−i5i5i5−i5000000-222-223−23−232300-111-1−i5i5i5−i500001+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ5900000000000000000000000000
χ734-4-44004-4-44-11-11−i5i5i5−i5000000-222-2−232323−2300-111-1−i5i5i5−i500001−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ4700000000000000000000000000
χ744-4-44004-4-44-11-11i5−i5−i5i50000004-4-44000000-111-1i5−i5−i5i50000-1-111-1-111i5−i5−i5i5−i5i5i5−i500000000000000000000000000
χ754-4-44004-4-44-11-11i5−i5−i5i5000000-222-223−23−232300-111-1i5−i5−i5i500001−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ4700000000000000000000000000
χ764-4-44004-4-44-11-11i5−i5−i5i5000000-222-2−232323−2300-111-1i5−i5−i5i500001+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ5900000000000000000000000000
χ7766-6-600-22-226-6-6600006i−6i6i−6i000000000000-22-220000−2i2i−2i2i000000000000000000000000000000000000000000
χ7866-6-600-22-226-6-660000−6i6i−6i6i000000000000-22-2200002i−2i2i−2i000000000000000000000000000000000000000000
χ796-6-6600-222-26-66-600006i−6i−6i6i000000000000-222-20000−2i2i2i−2i000000000000000000000000000000000000000000
χ806-6-6600-222-26-66-60000−6i6i6i−6i000000000000-222-200002i−2i−2i2i000000000000000000000000000000000000000000
χ81121212121212-4-4-4-4-3-3-3-3-3-3-3-30000-4-40000000000111111110000000000000000000000000000000000000000000000
χ8212121212-12-12-4-4-4-4-3-3-3-3333300004400000000001111-1-1-1-10000000000000000000000000000000000000000000000
χ831212-12-1200-44-44-333-3−3535−353500000000000000001-11-15−55−50000000000000000000000000000000000000000000000
χ841212-12-1200-44-44-333-335−3535−3500000000000000001-11-1−55−550000000000000000000000000000000000000000000000
χ8512-1212-1212i−12i-4-444-3-333−3i−3i3i3i0000−4i4i000000000011-1-1ii−i−i0000000000000000000000000000000000000000000000
χ8612-1212-12−12i12i-4-444-3-3333i3i−3i−3i00004i−4i000000000011-1-1−i−iii0000000000000000000000000000000000000000000000
χ8712-12-121200-444-4-33-33−3i53i53i5−3i500000000000000001-1-11i5−i5−i5i50000000000000000000000000000000000000000000000
χ8812-12-121200-444-4-33-333i5−3i5−3i53i500000000000000001-1-11−i5i5i5−i50000000000000000000000000000000000000000000000

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