Finite Group Databasebeta

← Group #14297582

Character table — Group #14297582

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222244444444444444444444666688888888888888888810101010121212121212121212121212121212121212202020202020404040404040404040404040404060606060120120120120
order12222236662256610101010101010101010101010101044446615303030303030303030303030303030444444202020202020202020202020202020202212121212668888242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ41111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−iii
χ5111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111−i−iii
χ8111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111ii−i−i
χ91111111111-1-1111111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11-11-111-1-111-1-111-1-11-11-1
χ101111111111-1-1111111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-1-111-1-11111-1-1-11-11
χ111111111111-1-1111111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111i−i−iiii−i−i−i−iii-1-111i−i−ii
χ121111111111-1-1111111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111−iii−i−i−iiiii−i−i-1-111−iii−i
χ131111111111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-111-1-111-1-1-1-111-11-11
χ141111111111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11-11-1-111-1-111-1-1111-11-1
χ151111111111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111i−i−iiii−i−i−i−iii11-1-1−iii−i
χ161111111111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111−iii−i−i−iiiii−i−i11-1-1i−i−ii
χ17222222-1-1-1-1222-1-12222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000000022-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ18222222-1-1-1-1222-1-12222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000000022-1-1-1-1-1-1-2-2-2-21111111100000000
χ19222222-1-1-1-1222-1-12222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000000-2-21111112i2i−2i−2i−i−i−i−iiiii00000000
χ20222222-1-1-1-1222-1-12222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000000-2-2111111−2i−2i2i2iiiii−i−i−i−i00000000
χ21222222-1-1-1-1-2-22-1-1222222-2-2-2-2-2-2-2-22000011-1-1-1-1-1-1-1-1111111112222000000000000000000-2-2-1-1-1-1112-22-2-1-111-1-11100000000
χ22222222-1-1-1-1-2-22-1-1222222-2-2-2-2-2-2-2-22000011-1-1-1-1-1-1-1-1111111112222000000000000000000-2-2-1-1-1-111-22-2211-1-111-1-100000000
χ23222222-1-1-1-1-2-22-1-1222222-2-2-2-2-2-2-2-22000011-1-1-1-1-1-1-1-111111111-2-2-2-2000000000000000000221111-1-12i−2i−2i2i−i−iiiii−i−i00000000
χ24222222-1-1-1-1-2-22-1-1222222-2-2-2-2-2-2-2-22000011-1-1-1-1-1-1-1-111111111-2-2-2-2000000000000000000221111-1-1−2i2i2i−2iii−i−i−i−iii00000000
χ252222-2-22222002-2-222-2-2-2-200000000222-2-2002222-2-2-2-2000000002-22-2002222-2-2-2-200000000002-22-2000000000000002-2000000
χ262222-2-22222002-2-222-2-2-2-200000000222-2-2002222-2-2-2-200000000-22-22002222-2-2-2-20000000000-22-2200000000000000-22000000
χ272222-2-22222002-2-222-2-2-2-2000000002-2-222002222-2-2-2-2000000002-22-200-2-2-2-2222200000000002-22-200000000000000-22000000
χ282222-2-22222002-2-222-2-2-2-2000000002-2-222002222-2-2-2-200000000-22-2200-2-2-2-222220000000000-22-22000000000000002-2000000
χ2922-2-22-22-2-220022-22-222-2-200000000-200000022-2-222-2-2000000002-2-222i−2i000000002i2i2i2i−2i−2i−2i−2i002-2-2200000000000000002i−2i0000
χ3022-2-22-22-2-220022-22-222-2-200000000-200000022-2-222-2-2000000002-2-22−2i2i00000000−2i−2i−2i−2i2i2i2i2i002-2-220000000000000000−2i2i0000
χ3122-2-22-22-2-220022-22-222-2-200000000-200000022-2-222-2-200000000-222-22i−2i000000002i2i2i2i−2i−2i−2i−2i00-222-20000000000000000−2i2i0000
χ3222-2-22-22-2-220022-22-222-2-200000000-200000022-2-222-2-200000000-222-2−2i2i00000000−2i−2i−2i−2i2i2i2i2i00-222-200000000000000002i−2i0000
χ3322-2-2-222-2-222-22-222-2-2-2222222-2-2-2-2-200002-222-2-2-2-2222222-2-2-2-222-2-20000000000000000002-222-2-22-200000000000000000000
χ3422-2-2-222-2-222-22-222-2-2-2222222-2-2-2-2-200002-222-2-2-2-2222222-2-2-2-2-2-222000000000000000000-22-2-222-2200000000000000000000
χ3522-2-2-222-2-22-222-222-2-2-222-2-2-2-22222-20000-2222-2-2-2-222-2-2-2-2222222-2-2000000000000000000-2222-2-2-2200000000000000000000
χ3622-2-2-222-2-22-222-222-2-2-222-2-2-2-22222-20000-2222-2-2-2-222-2-2-2-22222-2-2220000000000000000002-2-2-2222-200000000000000000000
χ3722-2-2-22-111-12-221-12-2-2-2222222-2-2-2-2-20000-11-1-11111-1-1-1-1-1-1111122-2-20000000000000000002-2-1-111-1100003−33−33−33−300000000
χ3822-2-2-22-111-12-221-12-2-2-2222222-2-2-2-2-20000-11-1-11111-1-1-1-1-1-1111122-2-20000000000000000002-2-1-111-110000−33−33−33−3300000000
χ3922-2-2-22-111-12-221-12-2-2-2222222-2-2-2-2-20000-11-1-11111-1-1-1-1-1-11111-2-222000000000000000000-2211-1-11-10000−i3i3−i3i3i3−i3i3−i300000000
χ4022-2-2-22-111-12-221-12-2-2-2222222-2-2-2-2-20000-11-1-11111-1-1-1-1-1-11111-2-222000000000000000000-2211-1-11-10000i3−i3i3−i3−i3i3−i3i300000000
χ4122-2-2-22-111-1-2221-12-2-2-222-2-2-2-22222-200001-1-1-11111-1-11111-1-1-1-122-2-2000000000000000000-22-1-1111-100003−3−333−3−3300000000
χ4222-2-2-22-111-1-2221-12-2-2-222-2-2-2-22222-200001-1-1-11111-1-11111-1-1-1-122-2-2000000000000000000-22-1-1111-10000−333−3−333−300000000
χ4322-2-2-22-111-1-2221-12-2-2-222-2-2-2-22222-200001-1-1-11111-1-11111-1-1-1-1-2-2220000000000000000002-211-1-1-110000−i3i3i3−i3i3−i3−i3i300000000
χ4422-2-2-22-111-1-2221-12-2-2-222-2-2-2-22222-200001-1-1-11111-1-11111-1-1-1-1-2-2220000000000000000002-211-1-1-110000i3−i3−i3i3−i3i3i3−i300000000
χ45444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ46444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-411111111111111110000000000000000000000000000
χ474444444444-4-4-144-1-1-1-1-1-111111111-14444-4-4-1-1-1-1-1-1-1-1111111110000-4-4-1-1-1-1-1-1-1-1111111110000000000000000000000000000
χ484444444444-4-4-144-1-1-1-1-1-111111111-1-4-4-4-4-4-4-1-1-1-1-1-1-1-11111111100004411111111-1-1-1-1-1-1-1-10000000000000000000000000000
χ494444-4-4444400-1-4-4-1-11111−5−555−5−555-144-4-400-1-1-1-11111−5−555−5−555000000-1-1-1-11111−5−555−5−5550000000000000000000000000000
χ504444-4-4444400-1-4-4-1-11111−5−555−5−555-1-4-44400-1-1-1-11111−5−555−5−5550000001111-1-1-1-155−5−555−5−50000000000000000000000000000
χ514444-4-4444400-1-4-4-1-1111155−5−555−5−5-144-4-400-1-1-1-1111155−5−555−5−5000000-1-1-1-1111155−5−555−5−50000000000000000000000000000
χ524444-4-4444400-1-4-4-1-1111155−5−555−5−5-1-4-44400-1-1-1-1111155−5−555−5−50000001111-1-1-1-1−5−555−5−5550000000000000000000000000000
χ534444-4-4-2-2-2-20042244-4-4-4-4000000004000000-2-2-2-22222000000004-44-400000000000000000000-22-220000000000000000000000
χ544444-4-4-2-2-2-20042244-4-4-4-4000000004000000-2-2-2-2222200000000-44-44000000000000000000002-22-20000000000000000000000
χ5544-4-44-44-4-4400-14-4-11-1-111−5−55555−5−51000000-1-111-1-111−5−55555−5−500004i−4i−i5−i5i5i5−i5−i5i5i5−i−i−i−iiiii0000000000000000000000000000
χ5644-4-44-44-4-4400-14-4-11-1-111−5−55555−5−51000000-1-111-1-111−5−55555−5−50000−4i4ii5i5−i5−i5i5i5−i5−i5iiii−i−i−i−i0000000000000000000000000000
χ5744-4-44-44-4-4400-14-4-11-1-11155−5−5−5−5551000000-1-111-1-11155−5−5−5−55500004i−4ii5i5−i5−i5i5i5−i5−i5−i−i−i−iiiii0000000000000000000000000000
χ5844-4-44-44-4-4400-14-4-11-1-11155−5−5−5−5551000000-1-111-1-11155−5−5−5−5550000−4i4i−i5−i5i5i5−i5−i5i5i5iiii−i−i−i−i0000000000000000000000000000
χ5944-4-44-4-222-2004-224-444-4-400000000-4000000-2-222-2-222000000004-4-4400000000000000000000-222-20000000000000000000000
χ6044-4-44-4-222-2004-224-444-4-400000000-4000000-2-222-2-22200000000-444-4000000000000000000002-2-220000000000000000000000
χ6144-4-4-444-4-444-4-1-44-1111-1-1-1-1-1-11111100004-4-1-11111-1-1-1-1-1-11111000000−i5−i5i5i5i5i5−i5−i5−i5−i5i5i5i5i5−i5−i50000000000000000000000000000
χ6244-4-4-444-4-444-4-1-44-1111-1-1-1-1-1-11111100004-4-1-11111-1-1-1-1-1-11111000000i5i5−i5−i5−i5−i5i5i5i5i5−i5−i5−i5−i5i5i50000000000000000000000000000
χ6344-4-4-444-4-44-44-1-44-1111-1-11111-1-1-1-110000-44-1-11111-1-11111-1-1-1-1000000−i5−i5i5i5i5i5−i5−i5i5i5−i5−i5−i5−i5i5i50000000000000000000000000000
χ6444-4-4-444-4-44-44-1-44-1111-1-11111-1-1-1-110000-44-1-11111-1-11111-1-1-1-1000000i5i5−i5−i5−i5−i5i5i5−i5−i5i5i5i5i5−i5−i50000000000000000000000000000
χ654-44-40044-4-400400-44000000000000-4004i−4i004-44-400000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ664-44-40044-4-400400-44000000000000-400−4i4i004-44-40000000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ674-44-40044-4-400-1001-1−55−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ581004i−4i00-11-11−55−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58000000−i5i5−i5i5−ii−iiζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ59ζ7−ζ11+ζ19−ζ23−ζ31−ζ43+ζ47+ζ59−ζ7+ζ11−ζ19+ζ23+ζ31+ζ43−ζ47−ζ59ζ7+ζ11−ζ19−ζ23+ζ31−ζ43+ζ47−ζ59−ζ7−ζ11+ζ19+ζ23−ζ31+ζ43−ζ47+ζ590000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.