Finite Group Databasebeta

← Group #13019052

Character table — Group #13019052

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111144444445555888888888816161616161616161620202032324040404040404040404040404040404040408080
order12224445101010444424888820202020204040404040404040244102024444488888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ411111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111-1-111-1-1111111111-1-1-1-1111-1-1-1-1111111-1-111-1-111-1-1-1-1
χ6111111111111111-1-111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ7111111111111111-1-1-1-11111111-1-1-1-11111111-1-1-1-11111-1-111-1-111-1-111-1-1
χ8111111111111111-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ911111111111-1-1-1-11111111111111111111-1-1-111-1-1ii−i−i-1-1-1-1i−ii−ii−ii−ii−i
χ1011111111111-1-1-1-11111111111111111111-1-1-111-1-1−i−iii-1-1-1-1−ii−ii−ii−ii−ii
χ1111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i1111−ii−ii−ii−iii−i
χ1211111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii1111i−ii−ii−ii−i−ii
χ1311111111111-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-111ii−i−i-1-111i−i−iii−i−ii−ii
χ1411111111111-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-111−i−iii-1-111−iii−i−iii−ii−i
χ1511111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-111ii−i−i11-1-1−iii−i−iii−i−ii
χ1611111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-111−i−iii11-1-1i−i−iii−i−iii−i
χ1722222-2-2222222222-20000-2-2-2-22000000002-2-22-2-22000000000000000000
χ1822222-2-222222222-220000-2-2-2-22000000002-2-2-222-2000000000000000000
χ1922222-2-22222-2-2-2-22-20000-2-2-2-2200000000-2222-22-2000000000000000000
χ2022222-2-22222-2-2-2-2-220000-2-2-2-2200000000-222-22-22000000000000000000
χ212222-22-22222222200000022-2-2-200000000-22-2000000000000002200-2-200
χ222222-22-22222222200000022-2-2-200000000-22-200000000000000-2-2002200
χ232222-22-22222-2-2-2-200000022-2-2-2000000002-22000000000000002i−2i00−2i2i00
χ242222-22-22222-2-2-2-200000022-2-2-2000000002-2200000000000000−2i2i002i−2i00
χ252222-2-2222222222000000-2-222-200000000-2-220000000000002200-2-20000
χ262222-2-2222222222000000-2-222-200000000-2-22000000000000-2-200220000
χ272222-2-222222-2-2-2-2000000-2-222-20000000022-20000000000002i−2i00−2i2i0000
χ282222-2-222222-2-2-2-2000000-2-222-20000000022-2000000000000−2i2i002i−2i0000
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
χ3744-4-400044-4-44i−4i4i−4i002-200000002-22-20000000000000002i−2i000000000000
χ3844-4-400044-4-44i−4i4i−4i00-220000000-22-22000000000000000−2i2i000000000000
χ3944-4-400044-4-4−4i4i−4i4i002-200000002-22-2000000000000000−2i2i000000000000
χ4044-4-400044-4-4−4i4i−4i4i00-220000000-22-220000000000000002i−2i000000000000
χ414-44-40004-44-44i−4i−4i4i00002i−2i0000000002i−2i2i−2i00000000000002-20000000000
χ424-44-40004-44-44i−4i−4i4i0000−2i2i000000000−2i2i−2i2i0000000000000-220000000000
χ434-44-40004-44-4−4i4i4i−4i00002i−2i0000000002i−2i2i−2i0000000000000-220000000000
χ444-44-40004-44-4−4i4i4i−4i0000−2i2i000000000−2i2i−2i2i00000000000002-20000000000
χ454-4-440004-4-4444-4-4000000000000000000000000002i−2i2i−2i00000000000000
χ464-4-440004-4-4444-4-400000000000000000000000000−2i2i−2i2i00000000000000
χ474-4-440004-4-44-4-444000000000000000000000000002-2-2200000000000000
χ484-4-440004-4-44-4-44400000000000000000000000000-222-200000000000000
χ498888-88-8-2-2-2-20000000000-2-2222000000000000000000000000000000000
χ508888-8-88-2-2-2-2000000000022-2-22000000000000000000000000000000000
χ5188-8-8000-2-2220000004-400002i5−2i50−1+i51−i5−1−i51+i500000000000000000000000000000
χ5288-8-8000-2-2220000004-40000−2i52i50−1−i51+i5−1+i51−i500000000000000000000000000000
χ5388-8-8000-2-222000000-4400002i5−2i501−i5−1+i51+i5−1−i500000000000000000000000000000
χ5488-8-8000-2-222000000-440000−2i52i501+i5−1−i51−i5−1+i500000000000000000000000000000
χ558-88-8000-22-22000000004i−4i2i5−2i50000000−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ190000000000000000000000000
χ568-88-8000-22-22000000004i−4i−2i52i50000000ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ190000000000000000000000000
χ578-88-8000-22-2200000000−4i4i2i5−2i50000000ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ19−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ190000000000000000000000000
χ588-88-8000-22-2200000000−4i4i−2i52i50000000−ζ2+ζ3+ζ6+ζ7+ζ11+ζ14−ζ18+ζ19ζ2−ζ3−ζ6−ζ7−ζ11−ζ14+ζ18−ζ19ζ2+ζ3−ζ6+ζ7+ζ11−ζ14+ζ18+ζ19−ζ2−ζ3+ζ6−ζ7−ζ11+ζ14−ζ18−ζ190000000000000000000000000
χ5916-16-1616000-444-4000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.