Finite Group Databasebeta

← Group #14299777

Character table — Group #14299777

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222444444444444558888888888888888888888101010101010101212202020202020202020202020244040404040404040404048484848606060606060120120120
order1223446664451012121212121220202210152020202020303030606060606060606060606060244666624444444121212121212844121212121212121210204040244444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111111-1-1111111111111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ5111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-111-1-1ii−i−i-1-1-1-1-1-11i−iiiii−i−i−i−i1111-1-1i−ii−i-1i−i
χ6111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-111-1-1−i−iii-1-1-1-1-1-11−ii−i−i−i−iiiii1111-1-1−ii−ii-1−ii
χ7111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1i−iiiii−i−i−i−i-1-1-1-111−ii−ii1−ii
χ8111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1−ii−i−i−i−iiiii-1-1-1-111i−ii−i1i−i
χ9111111111-1-11111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1
χ10111111111-1-11111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-111
χ11111111111-1-11111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1111
χ12111111111-1-11111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-111-1-111-1-111111-1-1
χ13111111111-1-11111-1-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i-1-11111-1−iiii−i−i−i−iii11-1-1-1-1i−ii−i1−ii
χ14111111111-1-11111-1-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii-1-11111-1i−i−i−iiiii−i−i11-1-1-1-1−ii−ii1i−i
χ15111111111-1-11111-1-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-1-111111−iiii−i−i−i−iii-1-11111−ii−ii-1i−i
χ16111111111-1-11111-1-1-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-1-111111i−i−i−iiiii−i−i-1-11111i−ii−i-1−ii
χ172222-2-22220022-2-20000-2-22222-20000222-2-2-2-2000000002-2-2222200002-22-2-2-200000002-2002-2000000000000000
χ182222-2-22220022-2-20000-2-22222-20000222-2-2-2-2000000002-2-222220000-22-22-2-20000000-2200-22000000000000000
χ192222-2-22220022-2-20000-2-2-2-222-20000222-2-2-2-200000000-222-2-2-2-200002i−2i−2i2i2200000002i−2i00−2i2i000000000000000
χ202222-2-22220022-2-20000-2-2-2-222-20000222-2-2-2-200000000-222-2-2-2-20000−2i2i2i−2i220000000−2i2i002i−2i000000000000000
χ21222-122-1-1-12222-1-1-1-1-1-122222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-100222222-1-1-1-1-1-1022-1-1-1-1-1-1-1-10000000000000
χ22222-122-1-1-12222-1-1-1-1-1-122222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-10022-2-2-2-2-1-1-1-1-1-10-2-2111111110000000000000
χ23222-122-1-1-12222-1-1-1-1-1-122-2-22-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111100-2-22i2i−2i−2i11111102i−2i−i−i−i−iiiii0000000000000
χ24222-122-1-1-12222-1-1-1-1-1-122-2-22-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111100-2-2−2i−2i2i2i1111110−2i2iiiii−i−i−i−i0000000000000
χ25222-122-1-1-1-2-222-1-1111122222-12-2-2-2-2-1-1-1-1-1-1-111111111222-1-1-1-100-2-22222-1-111110-2-2-1-111-1-1110000000000000
χ26222-122-1-1-1-2-222-1-1111122222-12-2-2-2-2-1-1-1-1-1-1-111111111222-1-1-1-100-2-2-2-2-2-2-1-1111102211-1-111-1-10000000000000
χ27222-122-1-1-1-2-222-1-1111122-2-22-12-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2111100222i2i−2i−2i11-1-1-1-10−2i2i−i−iiiii−i−i0000000000000
χ28222-122-1-1-1-2-222-1-1111122-2-22-12-2-2-2-2-1-1-1-1-1-1-111111111-2-2-211110022−2i−2i2i2i11-1-1-1-102i−2iii−i−i−i−iii0000000000000
χ29222-1-2-2-1-1-1002211−i3−i3i3i3-2-2222-1-20000-1-1-11111−i3−i3−i3−i3i3i3i3i32-2-2-1-1-1-100002-22-211−i3−i3i3i3000-11−i3i3-11−i3i30000000000000
χ30222-1-2-2-1-1-1002211−i3−i3i3i3-2-2222-1-20000-1-1-11111−i3−i3−i3−i3i3i3i3i32-2-2-1-1-1-10000-22-2211−i3−i3i3i30001-1i3−i31-1i3−i30000000000000
χ31222-1-2-2-1-1-1002211−i3−i3i3i3-2-2-2-22-1-20000-1-1-11111−i3−i3−i3−i3i3i3i3i3-222111100002i−2i−2i2i-1-1i3i3−i3−i3000−ii3−3i−i−330000000000000
χ32222-1-2-2-1-1-1002211−i3−i3i3i3-2-2-2-22-1-20000-1-1-11111−i3−i3−i3−i3i3i3i3i3-22211110000−2i2i2i−2i-1-1i3i3−i3−i3000i−i−33−ii3−30000000000000
χ33222-1-2-2-1-1-1002211i3i3−i3−i3-2-2222-1-20000-1-1-11111i3i3i3i3−i3−i3−i3−i32-2-2-1-1-1-100002-22-211i3i3−i3−i3000-11i3−i3-11i3−i30000000000000
χ34222-1-2-2-1-1-1002211i3i3−i3−i3-2-2222-1-20000-1-1-11111i3i3i3i3−i3−i3−i3−i32-2-2-1-1-1-10000-22-2211i3i3−i3−i30001-1−i3i31-1−i3i30000000000000
χ35222-1-2-2-1-1-1002211i3i3−i3−i3-2-2-2-22-1-20000-1-1-11111i3i3i3i3−i3−i3−i3−i3-222111100002i−2i−2i2i-1-1−i3−i3i3i3000−ii−33i−i3−30000000000000
χ36222-1-2-2-1-1-1002211i3i3−i3−i3-2-2-2-22-1-20000-1-1-11111i3i3i3i3−i3−i3−i3−i3-22211110000−2i2i2i−2i-1-1−i3−i3i3i3000i−i3−3−ii−330000000000000
χ3722-222-22-2-200222-20000-2-222-22200002-2-222-2-200000000-2-222-2-222-20000002-20000000000000002-2002-20000000
χ3822-222-22-2-200222-20000-2-222-22200002-2-222-2-200000000-2-222-2-22-220000002-2000000000000000-2200-220000000
χ3922-222-22-2-200222-20000-2-2-2-2-22200002-2-222-2-20000000022-2-222-22-2000000-220000000000000002-200-220000000
χ4022-222-22-2-200222-20000-2-2-2-2-22200002-2-222-2-20000000022-2-222-2-22000000-22000000000000000-22002-20000000
χ4122-22-222-2-20022-2200002222-22-200002-2-2-2-22200000000-22-22-2-2200000000-2200000000000000000000022-2-2000
χ4222-22-222-2-20022-2200002222-22-200002-2-2-2-22200000000-22-22-2-2200000000-22000000000000000000000-2-222000
χ4322-22-222-2-20022-22000022-2-2-22-200002-2-2-2-222000000002-22-222-2000000002-20000000000000000000002i−2i−2i2i000
χ4422-22-222-2-20022-22000022-2-2-22-200002-2-2-2-222000000002-22-222-2000000002-2000000000000000000000−2i2i2i−2i000
χ4544444444444-1-1444444-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000004400000000000040000000000-1-1-1-1000000000
χ4644444444444-1-1444444-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000-4-4000000000000-400000000001111000000000
χ47444444444-4-4-1-144-4-4-4-4-1-100-1-1-11111-1-1-1-1-1-1-111111111000000044000000000000-40000000000-1-111000000000
χ48444444444-4-4-1-144-4-4-4-4-1-100-1-1-11111-1-1-1-1-1-1-1111111110000000-4-40000000000004000000000011-1-1000000000
χ4944-444-44-4-400-1-14-4000011001-1-1−i5−i5i5i5-111-1-111−i5−i5i5i5−i5−i5i5i500000004-400000000000000000000000-11−i5i5000000000
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χ5144-444-44-4-400-1-14-4000011001-1-1i5i5−i5−i5-111-1-111i5i5−i5−i5i5i5−i5−i500000004-400000000000000000000000-11i5−i5000000000
χ5244-444-44-4-400-1-14-4000011001-1-1i5i5−i5−i5-111-1-111i5i5−i5−i5i5i5−i5−i50000000-44000000000000000000000001-1−i5i5000000000
χ5344-4-24-4-2220044-220000-4-444-4-240000-222-2-22200000000-4-44-222-200000000-220000000000000000000000000000
χ5444-4-24-4-2220044-220000-4-4-4-4-4-240000-222-2-2220000000044-42-2-22000000002-20000000000000000000000000000
χ5544-4-2-44-22200442-200004444-4-2-40000-22222-2-200000000-44-4-222-2000000002-20000000000000000000000000000
χ5644-4-2-44-22200442-2000044-4-4-4-2-40000-22222-2-2000000004-442-2-2200000000-220000000000000000000000000000
χ574-40400-4002-24-4002-22-2004-40402-22-2-40000002-22-22-22-2000400-4002-20000002-22-2000000000000000000000000
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χ594-40400-400-224-400-22-22004-4040-22-22-4000000-22-22-22-22000400-400-22000000-22-22000000000000000000000000
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χ634-40-2002−2i32i3-224-4001+i3−1−i31−i3−1+i3004-40-20-22-222−2i32i300001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000-2−2i32i3200-220000001+i3−1−i31−i3−1+i3000000000000000000000000
χ644-40-2002−2i32i3-224-4001+i3−1−i31−i3−1+i300-440-20-22-222−2i32i300001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i300022i3−2i3-2002-2000000−1−i31+i3−1+i31−i3000000000000000000000000
χ654-40-20022i3−2i32-24-400−1+i31−i3−1−i31+i3004-40-202-22-222i3−2i30000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000-22i3−2i32002-2000000−1+i31−i3−1−i31+i3000000000000000000000000
χ664-40-20022i3−2i32-24-400−1+i31−i3−1−i31+i300-440-202-22-222i3−2i30000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30002−2i32i3-200-220000001−i3−1+i31+i3−1−i3000000000000000000000000
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χ868-80-4004−4i34i3-44-22002+2i3−2−2i32−2i3−2+2i32i5−2i5000101−i5−1+i51+i5−1−i5-1i3−i315−15−i5i5ζ11+ζ22−ζ23+ζ34+ζ46−ζ47+ζ58+ζ59−ζ11−ζ22+ζ23−ζ34−ζ46+ζ47−ζ58−ζ59−ζ11+ζ22+ζ23+ζ34+ζ46+ζ47+ζ58−ζ59ζ11−ζ22−ζ23−ζ34−ζ46−ζ47−ζ58+ζ59ζ2−ζ7+ζ14+ζ19+ζ26+ζ31+ζ38−ζ43−ζ2+ζ7−ζ14−ζ19−ζ26−ζ31−ζ38+ζ43ζ2+ζ7+ζ14−ζ19+ζ26−ζ31+ζ38+ζ43−ζ2−ζ7−ζ14+ζ19−ζ26+ζ31−ζ38−ζ43000000000000000000000000000000000000000000000
χ878-80-40044i3−4i34-4-2200−2+2i32−2i3−2−2i32+2i3−2i52i500010−1−i51+i5−1+i51−i5-1−i3i315−15i5−i5−ζ2−ζ7−ζ14+ζ19−ζ26+ζ31−ζ38−ζ43ζ2+ζ7+ζ14−ζ19+ζ26−ζ31+ζ38+ζ43−ζ2+ζ7−ζ14−ζ19−ζ26−ζ31−ζ38+ζ43ζ2−ζ7+ζ14+ζ19+ζ26+ζ31+ζ38−ζ43ζ11−ζ22−ζ23−ζ34−ζ46−ζ47−ζ58+ζ59−ζ11+ζ22+ζ23+ζ34+ζ46+ζ47+ζ58−ζ59−ζ11−ζ22+ζ23−ζ34−ζ46+ζ47−ζ58−ζ59ζ11+ζ22−ζ23+ζ34+ζ46−ζ47+ζ58+ζ59000000000000000000000000000000000000000000000
χ888-80-40044i3−4i34-4-2200−2+2i32−2i3−2−2i32+2i32i5−2i500010−1+i51−i5−1−i51+i5-1−i3i3−1515−i5i5−ζ2+ζ7−ζ14−ζ19−ζ26−ζ31−ζ38+ζ43ζ2−ζ7+ζ14+ζ19+ζ26+ζ31+ζ38−ζ43−ζ2−ζ7−ζ14+ζ19−ζ26+ζ31−ζ38−ζ43ζ2+ζ7+ζ14−ζ19+ζ26−ζ31+ζ38+ζ43−ζ11−ζ22+ζ23−ζ34−ζ46+ζ47−ζ58−ζ59ζ11+ζ22−ζ23+ζ34+ζ46−ζ47+ζ58+ζ59ζ11−ζ22−ζ23−ζ34−ζ46−ζ47−ζ58+ζ59−ζ11+ζ22+ζ23+ζ34+ζ46+ζ47+ζ58−ζ59000000000000000000000000000000000000000000000
χ898-80-40044i3−4i3-44-22002−2i3−2+2i32+2i3−2−2i3−2i52i5000101+i5−1−i51−i5−1+i5-1−i3i315−15i5−i5ζ2+ζ7+ζ14−ζ19+ζ26−ζ31+ζ38+ζ43−ζ2−ζ7−ζ14+ζ19−ζ26+ζ31−ζ38−ζ43ζ2−ζ7+ζ14+ζ19+ζ26+ζ31+ζ38−ζ43−ζ2+ζ7−ζ14−ζ19−ζ26−ζ31−ζ38+ζ43−ζ11+ζ22+ζ23+ζ34+ζ46+ζ47+ζ58−ζ59ζ11−ζ22−ζ23−ζ34−ζ46−ζ47−ζ58+ζ59ζ11+ζ22−ζ23+ζ34+ζ46−ζ47+ζ58+ζ59−ζ11−ζ22+ζ23−ζ34−ζ46+ζ47−ζ58−ζ59000000000000000000000000000000000000000000000
χ908-80-40044i3−4i3-44-22002−2i3−2+2i32+2i3−2−2i32i5−2i5000101−i5−1+i51+i5−1−i5-1−i3i3−1515−i5i5ζ2−ζ7+ζ14+ζ19+ζ26+ζ31+ζ38−ζ43−ζ2+ζ7−ζ14−ζ19−ζ26−ζ31−ζ38+ζ43ζ2+ζ7+ζ14−ζ19+ζ26−ζ31+ζ38+ζ43−ζ2−ζ7−ζ14+ζ19−ζ26+ζ31−ζ38−ζ43ζ11+ζ22−ζ23+ζ34+ζ46−ζ47+ζ58+ζ59−ζ11−ζ22+ζ23−ζ34−ζ46+ζ47−ζ58−ζ59−ζ11+ζ22+ζ23+ζ34+ζ46+ζ47+ζ58−ζ59ζ11−ζ22−ζ23−ζ34−ζ46−ζ47−ζ58+ζ59000000000000000000000000000000000000000000000

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