Finite Group Databasebeta

← Group #13019049

Character table — Group #13019049

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111144444445555888888888816161616161616161620202032324040404040404040404040404040404040408080
order12224445101010444444888820202020204040404040404040244202024888888888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-111-1-1111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ6111111111111111-1-111-1-1111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-111111111-1-1
χ911111111111-1-1-1-11111111111111111111-1-1-111-1-1-1-1-1-1ii−i−iii−i−iii−i−ii−i
χ1011111111111-1-1-1-11111111111111111111-1-1-111-1-1-1-1-1-1−i−iii−i−iii−i−iii−ii
χ1111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−ii
χ1211111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−ii−i
χ1311111111111-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−ii
χ1411111111111-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiii−i
χ1511111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iiii−i
χ1611111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−ii
χ1722222-2-2222222222-20000-2-2-2-2200000000-2-222-22-2000000000000000000
χ1822222-2-222222222-220000-2-2-2-2200000000-2-22-22-22000000000000000000
χ1922222-2-22222-2-2-2-22-20000-2-2-2-220000000022-22-2-22000000000000000000
χ2022222-2-22222-2-2-2-2-220000-2-2-2-220000000022-2-222-2000000000000000000
χ212222-22-22222222200000022-2-2-2000000002-2-20000000000002-22-2000000
χ222222-22-22222222200000022-2-2-2000000002-2-2000000000000-22-22000000
χ232222-22-22222-2-2-2-200000022-2-2-200000000-2220000000000002i−2i−2i2i000000
χ242222-22-22222-2-2-2-200000022-2-2-200000000-222000000000000−2i2i2i−2i000000
χ252222-2-2222222222000000-2-222-200000000-22-2000000002-22-20000000000
χ262222-2-2222222222000000-2-222-200000000-22-200000000-22-220000000000
χ272222-2-222222-2-2-2-2000000-2-222-2000000002-22000000002i−2i−2i2i0000000000
χ282222-2-222222-2-2-2-2000000-2-222-2000000002-2200000000−2i2i2i−2i0000000000
χ294444444-1-1-1-10000444444-1-1-1-1-1-1-1-1-1-1-1-1-1000-1-100000000000000000000
χ304444444-1-1-1-1000044-4-4-4-4-1-1-1-1-111111111000-1-100000000000000000000
χ314444444-1-1-1-10000-4-444-4-4-1-1-1-1-1-1-1-1-111110001100000000000000000000
χ324444444-1-1-1-10000-4-4-4-444-1-1-1-1-11111-1-1-1-10001100000000000000000000
χ3344444-4-4-1-1-1-100004-400001111-1i5i5−i5−i5i5i5−i5−i5000-1100000000000000000000
χ3444444-4-4-1-1-1-100004-400001111-1−i5−i5i5i5−i5−i5i5i5000-1100000000000000000000
χ3544444-4-4-1-1-1-10000-4400001111-1i5i5−i5−i5−i5−i5i5i50001-100000000000000000000
χ3644444-4-4-1-1-1-10000-4400001111-1−i5−i5i5i5i5i5−i5−i50001-100000000000000000000
χ3744-4-40004-44-444-4-4002i−2i00000002i−2i2i−2i000000000002i−2i0000000000000000
χ3844-4-40004-44-444-4-400−2i2i0000000−2i2i−2i2i00000000000−2i2i0000000000000000
χ3944-4-40004-44-4-4-444002i−2i00000002i−2i2i−2i00000000000−2i2i0000000000000000
χ4044-4-40004-44-4-4-44400−2i2i0000000−2i2i−2i2i000000000002i−2i0000000000000000
χ414-44-40004-4-444i−4i4i−4i00002-20000000002-22-20000000002i−2i00000000000000
χ424-44-40004-4-444i−4i4i−4i0000-22000000000-22-22000000000−2i2i00000000000000
χ434-44-40004-4-44−4i4i−4i4i00002-20000000002-22-2000000000−2i2i00000000000000
χ444-44-40004-4-44−4i4i−4i4i0000-22000000000-22-220000000002i−2i00000000000000
χ454-4-4400044-4-44i−4i−4i4i00000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ464-4-4400044-4-44i−4i−4i4i000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ474-4-4400044-4-4−4i4i4i−4i00000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ484-4-4400044-4-4−4i4i4i−4i000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ498888-88-8-2-2-2-20000000000-2-2222000000000000000000000000000000000
χ508888-8-88-2-2-2-2000000000022-2-22000000000000000000000000000000000
χ5188-8-8000-22-220000004i−4i00002i5−2i50ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ3800000000000000000000000000000
χ5288-8-8000-22-220000004i−4i0000−2i52i50−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ3800000000000000000000000000000
χ5388-8-8000-22-22000000−4i4i00002i5−2i50−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ3800000000000000000000000000000
χ5488-8-8000-22-22000000−4i4i0000−2i52i50ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ3800000000000000000000000000000
χ558-88-8000-222-2000000004-42i5−2i50000000−1+i51−i5−1−i51+i50000000000000000000000000
χ568-88-8000-222-2000000004-4−2i52i50000000−1−i51+i5−1+i51−i50000000000000000000000000
χ578-88-8000-222-200000000-442i5−2i500000001−i5−1+i51+i5−1−i50000000000000000000000000
χ588-88-8000-222-200000000-44−2i52i500000001+i5−1−i51−i5−1+i50000000000000000000000000
χ5916-16-1616000-4-444000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.