Finite Group Databasebeta

← Group #14313184

Character table — Group #14313184

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1122244444488888888121212121515161616161616161616202020202424242430404040404040404048486080808080120120120120120
order12236256101010461010153030302444441220203030606060602224202020204446668812102041212242444488
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1111-1-11111-1-1-1-11-1-1-1-1
χ311111111111111111111111-1-1111111111-1-1-1-11111-1i−i-1-1-1i−i-111-1i−ii−i-1i−ii−i
χ411111111111111111111111-1-1111111111-1-1-1-11111-1−ii-1-1-1−ii-111-1−ii−ii-1−ii−ii
χ51111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11i−i-1-1-1i−i-1-1-11i−ii−i1−ii−ii
χ61111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-11−ii-1-1-1−ii-1-1-11−ii−ii1i−ii−i
χ71111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-111111111-1-1-11111-1-1-1-1-1
χ81111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111
χ911111111111-1111111111-1-111-1-1-111-1-1-1-1-1-111-1-1-1-1111-1-11-1-1111111-1-1-111-1-1
χ1011111111111-1111111111-1-111-1-1-111-1-1-1-1-1-111-1-1-1-11-1-1-1-11111111-1-111-1-1-111
χ1111111111111-1111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1i−i11-1−ii-111-1i−i−ii1i−i−ii
χ1211111111111-1111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1−ii11-1i−i-111-1−iii−i1−iii−i
χ1311111111111-11111111-1-11111-1-1-111-1-1-1-111-1-111111i−i11-1−ii-1-1-11i−i−ii-1−iii−i
χ1411111111111-11111111-1-11111-1-1-111-1-1-1-111-1-111111−ii11-1i−i-1-1-11−iii−i-1i−i−ii
χ1511111111111-11111111-1-111-1-1-1-1-111-1-1-1-1-1-1111111-111-1-11-1-11-1-1-111-1-11-1-111
χ1611111111111-11111111-1-111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-111111-1-1
χ1722222-2222220-2-2-222222-20022000-2-2000000-22000020000-20022-2-2000000000
χ1822222-2222220-2-2-222222-200-2-2000-2-20000002-20000-20000200-22-22000000000
χ1922222-2222220-2-2-22222-220022000-2-20000002-2000020000200-2-22-2000000000
χ2022222-2222220-2-2-22222-2200-2-2000-2-2000000-220000-20000-2002-222000000000
χ21222-1-122-12222-122-1-1-1-1000000-122-1-1-1-1-1-122220000022-1-1-122-1000-1-1-1-100000
χ22222-1-122-12222-122-1-1-1-1000000-122-1-1-1-1-1-1222200000-2-2-1-1-1-2-2-1000111100000
χ23222-1-122-12222-122-1-1-1-1000000-122-1-1-1-1-1-1-2-2-2-2000002i−2i1112i−2i1000−ii−ii00000
χ24222-1-122-12222-122-1-1-1-1000000-122-1-1-1-1-1-1-2-2-2-200000−2i2i111−2i2i1000i−ii−i00000
χ25222-1-122-1222-2-122-1-1-1-10000001-2-2-1-1111122-2-2000002i−2i-1-11−2i2i1000−iii−i00000
χ26222-1-122-1222-2-122-1-1-1-10000001-2-2-1-1111122-2-200000−2i2i-1-112i−2i1000i−i−ii00000
χ27222-1-122-1222-2-122-1-1-1-10000001-2-2-1-11111-2-222000002211-1-2-2-1000-1-11100000
χ28222-1-122-1222-2-122-1-1-1-10000001-2-2-1-11111-2-22200000-2-211-122-100011-1-100000
χ29444444-14-1-1-144-1-1-1-1-1-14444004-1-1-1-1-1-1-1-10000-1-1-1-1000000000-1-10000000000
χ30444444-14-1-1-144-1-1-1-1-1-1-4-4-4-4004-1-1-1-1-1-1-1-100001111000000000110000000000
χ31444444-14-1-1-1-44-1-1-1-1-1-144-4-400-411-1-1111100001111000000000-1-10000000000
χ32444444-14-1-1-1-44-1-1-1-1-1-1-4-44400-411-1-111110000-1-1-1-1000000000110000000000
χ3344444-4-14-1-1-10-411-1-1-1-14-400000−5511−5−5550000−5−555000000000-110000000000
χ3444444-4-14-1-1-10-411-1-1-1-14-4000005−51155−5−5000055−5−5000000000-110000000000
χ3544444-4-14-1-1-10-411-1-1-1-1-4400000−5511−5−555000055−5−50000000001-10000000000
χ3644444-4-14-1-1-10-411-1-1-1-1-44000005−51155−5−50000−5−5550000000001-10000000000
χ37444-2-2-44-244402-4-4-2-2-2-2000000000220000004-4000000000-2002000000000000
χ38444-2-2-44-244402-4-4-2-2-2-200000000022000000-44000000000200-2000000000000
χ3944-44404-4-4-44000044-4-400004400000000000000000-400000000000000000000
χ4044-44404-4-4-44000044-4-40000-4-400000000000000000400000000000000000000
χ414-404-404000-400004-400002i−2i4i−4i0000000002-2002i−2i2i−2i0002-20000000000000000
χ424-404-404000-400004-400002i−2i−4i4i000000000-22002i−2i2i−2i000-220000000000000000
χ434-404-404000-400004-40000−2i2i4i−4i000000000-2200−2i2i−2i2i000-220000000000000000
χ444-404-404000-400004-40000−2i2i−4i4i0000000002-200−2i2i−2i2i0002-20000000000000000
χ45888-4-48-2-4-2-2-28-4-2-21111000000-4-2-211111100000000000000000000000000000
χ46888-4-48-2-4-2-2-2-8-4-2-2111100000042211-1-1-1-100000000000000000000000000000
χ47888-4-4-8-2-4-2-2-2042211110000000−2525-1-155−5−500000000000000000000000000000
χ48888-4-4-8-2-4-2-2-204221111000000025−25-1-1−5−55500000000000000000000000000000
χ4988-8880-2-822-200−2525-2-222000000000−2525000000000000000000000000000000000
χ5088-8880-2-822-20025−25-2-22200000000025−25000000000000000000000000000000000
χ5188-8-4-4084-8-880000-4-44400000000000000000000000000000000000000000000
χ5288-8-4-40-2422-200−252511-1-10000000005−5ζ7+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+ζ5900000000000000000000000000000
χ5388-8-4-40-2422-200−252511-1-10000000005−5−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−ζ5900000000000000000000000000000
χ5488-8-4-40-2422-20025−2511-1-1000000000−55−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−ζ5900000000000000000000000000000
χ5588-8-4-40-2422-20025−2511-1-1000000000−55ζ7−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+ζ5900000000000000000000000000000
χ568-808-80-20−252520000-22−2525004i−4i000000000000000−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47000000000000000000000
χ578-808-80-20−252520000-22−252500−4i4i0000000000000002ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ592ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ47000000000000000000000
χ588-808-80-2025−2520000-2225−25004i−4i000000000000000−2ζ7−2ζ23−2ζ43−2ζ472ζ7+2ζ23+2ζ43+2ζ47−2ζ11−2ζ19−2ζ31−2ζ592ζ11+2ζ19+2ζ31+2ζ59000000000000000000000
χ598-808-80-2025−2520000-2225−2500−4i4i0000000000000002ζ7+2ζ23+2ζ43+2ζ47−2ζ7−2ζ23−2ζ43−2ζ472ζ11+2ζ19+2ζ31+2ζ59−2ζ11−2ζ19−2ζ31−2ζ59000000000000000000000
χ608-80-4408000-80000-44000000000000000004-4000000000-220000000000000000
χ618-80-4408000-80000-4400000000000000000-440000000002-20000000000000000
χ6216-160-880-40−4545400002-225−2500000000000000000000000000000000000000000000
χ6316-160-880-4045−45400002-2−252500000000000000000000000000000000000000000000

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