Finite Group Databasebeta

← Group #14284261

Character table — Group #14284261

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222244444668888888810101010121616161616161616162020202020202020242424242430303030404040404040404040404048486060606080120120120
order12223666451010104441215202030303044444122020606060606060888812121212420202020224448824242424242424242020888812488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ311111111111111111111111-1-1-1-11111111111ii−i−i-1-1-1-111111-1-1-1-1-1i−iiiii−i−i−i−i11ii−i−i-1-1i−i
χ411111111111111111111111-1-1-1-11111111111−i−iii-1-1-1-111111-1-1-1-1-1−ii−i−i−i−iiiii11−i−iii-1-1−ii
χ5111111111111111-1111111111111-1-1-111-1-1-1-111111111-111111111-1-1-111-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-111111111-111-1-111-1-111-1-1-1-1-1-1-1-111
χ7111111111111111-11111111-1-1-1-11-1-1-111-1-1-1-1ii−i−i-1-1-1-1-11111-1-1-1-11−iiii−i−i−i−iii-1-1ii−i−i11−ii
χ8111111111111111-11111111-1-1-1-11-1-1-111-1-1-1-1−i−iii-1-1-1-1-11111-1-1-1-11i−i−i−iiiii−i−i-1-1−i−iii11i−i
χ91111111111111-1-1111111111111-111111111111111111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11-1-1-1
χ101111111111111-1-1111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111-111
χ111111111111111-1-111111111-1-1-1-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-11111-1i−iiiii−i−i−i−i-1-1−i−iii-11−ii
χ121111111111111-1-111111111-1-1-1-1-1111111111−i−iii-1-1-1-1-1-1-1-1-11111-1−ii−i−i−i−iiiii-1-1ii−i−i-11i−i
χ131111111111111-1-1-111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1111
χ141111111111111-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111-1-111-1-111111111-11-1-1
χ151111111111111-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i-1-1-1-11-1-1-1-111111−iiii−i−i−i−iii11−i−iii1-1i−i
χ161111111111111-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1−i−iii-1-1-1-11-1-1-1-111111i−i−i−iiiii−i−i11ii−i−i1-1−ii
χ1722222222-22222220-22-2-222222-2-2-2000-2-20000000022-2-2022-2-2-2-222000000000000000000000
χ1822222222-22222220-22-2-2222-2-222-2000-2-200000000-2-222022-2-222-2-2000000000000000000000
χ1922222222-22222-2-20-22-2-222222-2-22000-2-20000000022-2-20-2-22222-2-2000000000000000000000
χ2022222222-22222-2-20-22-2-2222-2-2222000-2-200000000-2-2220-2-222-2-222000000000000000000000
χ212222-1-1-1-122222002-1-122-1-1-122220-122-1-1-1-1-1-12222-1-1-1-1000000000222-1-1-1-1-1-1-1-1000000-1000
χ222222-1-1-1-122222002-1-122-1-1-122220-122-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000002-2-211111111000000-1000
χ232222-1-1-1-122222002-1-122-1-1-1-2-2-2-20-122-1-1-1-1-1-12i2i−2i−2i1111000000000-22i−2i−i−i−i−iiiii0000001000
χ242222-1-1-1-122222002-1-122-1-1-1-2-2-2-20-122-1-1-1-1-1-1−2i−2i2i2i1111000000000-2−2i2iiiii−i−i−i−i0000001000
χ252222-1-1-1-12222200-2-1-122-1-1-1222201-2-2-1-111112222-1-1-1-1000000000-2-2-2-1-111-1-1110000001000
χ262222-1-1-1-12222200-2-1-122-1-1-1222201-2-2-1-11111-2-2-2-2-1-1-1-1000000000-22211-1-111-1-10000001000
χ272222-1-1-1-12222200-2-1-122-1-1-1-2-2-2-201-2-2-1-111112i2i−2i−2i11110000000002−2i2i−i−iiiii−i−i000000-1000
χ282222-1-1-1-12222200-2-1-122-1-1-1-2-2-2-201-2-2-1-11111−2i−2i2i2i111100000000022i−2iii−i−i−i−iii000000-1000
χ292-2-222-2-2202-22-22-2002002-2-22i−2i0000000000001+i−1−i1−i−1+i2i−2i0002-200002i−2i0001+i−1−i001−i−1+i00001+i−1−i1−i−1+i0000
χ302-2-222-2-2202-22-22-2002002-2-22i−2i000000000000−1−i1+i−1+i1−i2i−2i0002-200002i−2i000−1−i1+i00−1+i1−i0000−1−i1+i−1+i1−i0000
χ312-2-222-2-2202-22-22-2002002-2-2−2i2i0000000000001−i−1+i1+i−1−i−2i2i0002-20000−2i2i0001−i−1+i001+i−1−i00001−i−1+i1+i−1−i0000
χ322-2-222-2-2202-22-22-2002002-2-2−2i2i000000000000−1+i1−i−1−i1+i−2i2i0002-20000−2i2i000−1+i1−i00−1−i1+i0000−1+i1−i−1−i1+i0000
χ332-2-222-2-2202-22-2-22002002-2-22i−2i0000000000001+i−1−i1−i−1+i2i−2i000-220000−2i2i0001+i−1−i001−i−1+i0000−1−i1+i−1+i1−i0000
χ342-2-222-2-2202-22-2-22002002-2-22i−2i000000000000−1−i1+i−1+i1−i2i−2i000-220000−2i2i000−1−i1+i00−1+i1−i00001+i−1−i1−i−1+i0000
χ352-2-222-2-2202-22-2-22002002-2-2−2i2i0000000000001−i−1+i1+i−1−i−2i2i000-2200002i−2i0001−i−1+i001+i−1−i0000−1+i1−i−1−i1+i0000
χ362-2-222-2-2202-22-2-22002002-2-2−2i2i000000000000−1+i1−i−1−i1+i−2i2i000-2200002i−2i000−1+i1−i00−1−i1+i00001−i−1+i1+i−1−i0000
χ37444444444-1-1-1-14444-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1000000004-1-1-1-1000000000000000-1-100000000
χ38444444444-1-1-1-144-44-1-1-1-1-1-100004-411-1-1111100000000-4-1-1-1-10000000000000001100000000
χ39444444444-1-1-1-1-4-444-1-1-1-1-1-10000-44-1-1-1-1-1-1-1-100000000-411110000000000000001100000000
χ40444444444-1-1-1-1-4-4-44-1-1-1-1-1-10000-4-411-1-111110000000041111000000000000000-1-100000000
χ4144444444-4-1-1-1-1440-4-111-1-1-10000-40−5511−5−555000000000-1-111000000000000000−5500000000
χ4244444444-4-1-1-1-1440-4-111-1-1-10000-405−51155−5−5000000000-1-1110000000000000005−500000000
χ4344444444-4-1-1-1-1-4-40-4-111-1-1-1000040−5511−5−55500000000011-1-10000000000000005−500000000
χ4444444444-4-1-1-1-1-4-40-4-111-1-1-10000405−51155−5−500000000011-1-1000000000000000−5500000000
χ454444-2-2-2-2-444440002-2-4-4-2-2-244-4-400002200000000-2-222000000000000000000000000000000
χ464444-2-2-2-2-444440002-2-4-4-2-2-2-4-4440000220000000022-2-2000000000000000000000000000000
χ4744-4-444-4-4044-4-40000400-44-40000000000000000000000000004-400000000000000000000000
χ4844-4-444-4-4044-4-40000400-44-4000000000000000000000000000-4400000000000000000000000
χ494-44-44-44-404-4-440000400-4-44004i−4i00000000000000004i−4i000000000000000000000000000000
χ504-44-44-44-404-4-440000400-4-4400−4i4i0000000000000000−4i4i000000000000000000000000000000
χ514-44-4-22-2204-4-440000-20022-2004i−4i0000000000000000−2i2i00000000000000−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ5900−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ59ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ590000000000
χ524-44-4-22-2204-4-440000-20022-2004i−4i0000000000000000−2i2i00000000000000ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ5900ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ590000000000
χ534-44-4-22-2204-4-440000-20022-200−4i4i00000000000000002i−2i00000000000000−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ59ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ5900−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ59ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ590000000000
χ544-44-4-22-2204-4-440000-20022-200−4i4i00000000000000002i−2i00000000000000ζ2−ζ7+ζ11+ζ14−ζ19−ζ22+ζ23+ζ26−ζ31−ζ34+ζ38−ζ43−ζ46+ζ47−ζ58+ζ59−ζ2+ζ7−ζ11−ζ14+ζ19+ζ22−ζ23−ζ26+ζ31+ζ34−ζ38+ζ43+ζ46−ζ47+ζ58−ζ5900ζ2+ζ7−ζ11+ζ14+ζ19−ζ22−ζ23+ζ26+ζ31−ζ34+ζ38+ζ43−ζ46−ζ47−ζ58−ζ59−ζ2−ζ7+ζ11−ζ14−ζ19+ζ22+ζ23−ζ26−ζ31+ζ34−ζ38−ζ43+ζ46+ζ47+ζ58+ζ590000000000
χ554-4-44-222-204-44-40000-200-2224i−4i0000000000002+2i−2−2i2−2i−2+2i−2i2i00000000000000−1−i1+i00−1+i1−i000000000000
χ564-4-44-222-204-44-40000-200-2224i−4i000000000000−2−2i2+2i−2+2i2−2i−2i2i000000000000001+i−1−i001−i−1+i000000000000
χ574-4-44-222-204-44-40000-200-222−4i4i0000000000002−2i−2+2i2+2i−2−2i2i−2i00000000000000−1+i1−i00−1−i1+i000000000000
χ584-4-44-222-204-44-40000-200-222−4i4i000000000000−2+2i2−2i−2−2i2+2i2i−2i000000000000001−i−1+i001+i−1−i000000000000
χ598888-4-4-4-48-2-2-2-2008-41-2-211100000-4-2-211111100000000000000000000000000000000000000
χ608888-4-4-4-48-2-2-2-200-8-41-2-21110000042211-1-1-1-100000000000000000000000000000000000000
χ618888-4-4-4-4-8-2-2-2-20004122111000000−2525-1-155−5−500000000000000000000000000000000000000
χ628888-4-4-4-4-8-2-2-2-2000412211100000025−25-1-1−5−55500000000000000000000000000000000000000
χ6388-8-888-8-80-2-2220000-2−25252-2200000000−2525000000000000000000000000000000000000000000
χ6488-8-888-8-80-2-2220000-225−252-220000000025−25000000000000000000000000000000000000000000
χ6588-8-8-4-444088-8-80000-4004-440000000000000000000000000000000000000000000000000000
χ6688-8-8-4-4440-2-22200001−2525-11-1000000005−5ζ7+ζ11+ζ19+ζ23−ζ31−ζ43−ζ47−ζ59−ζ7−ζ11−ζ19−ζ23+ζ31+ζ43+ζ47+ζ59−ζ7+ζ11+ζ19−ζ23−ζ31+ζ43+ζ47−ζ59ζ7−ζ11−ζ19+ζ23+ζ31−ζ43−ζ47+ζ5900000000000000000000000000000000000000
χ6788-8-8-4-4440-2-22200001−2525-11-1000000005−5−ζ7−ζ11−ζ19−ζ23+ζ31+ζ43+ζ47+ζ59ζ7+ζ11+ζ19+ζ23−ζ31−ζ43−ζ47−ζ59ζ7−ζ11−ζ19+ζ23+ζ31−ζ43−ζ47+ζ59−ζ7+ζ11+ζ19−ζ23−ζ31+ζ43+ζ47−ζ5900000000000000000000000000000000000000
χ6888-8-8-4-4440-2-2220000125−25-11-100000000−55−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−ζ5900000000000000000000000000000000000000
χ6988-8-8-4-4440-2-2220000125−25-11-100000000−55ζ7−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+ζ5900000000000000000000000000000000000000
χ708-88-88-88-80-222-20000-20022-20000000000000000000000000−25250000000000000000000000000
χ718-88-88-88-80-222-20000-20022-2000000000000000000000000025−250000000000000000000000000
χ728-8-888-8-880-22-228-800-200-22200000000000000000000000-22000000000000000000000000000
χ738-8-888-8-880-22-22-8800-200-222000000000000000000000002-2000000000000000000000000000
χ7416-1616-16-88-880-444-40000200-2-220000000000000000000000000000000000000000000000000000
χ7516-16-1616-888-80-44-4400002002-2-20000000000000000000000000000000000000000000000000000

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