Finite Group Databasebeta

← Group #1200

Character table — Group #1200

Order 120.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24
size1122222233444455666610101515
order123556101044151530304420202020121222
χ1111111111111111111111111
χ211111111111111-1-11111-1-1-1-1
χ311111111-1-1111111-1-1-1-111-1-1
χ411111111-1-11111-1-1-1-1-1-1-1-111
χ51-1111-1-1-1i−i11-1-1i−iii−i−ii−i1-1
χ61-1111-1-1-1i−i11-1-1−iiii−i−i−ii-11
χ71-1111-1-1-1−ii11-1-1i−i−i−iiii−i-11
χ81-1111-1-1-1−ii11-1-1−ii−i−iii−ii1-1
χ9222−1+52−1−522−1+52−1−5222−1+52−1−52−1+52−1−5200−1+52−1−52−1+52−1−520000
χ10222−1+52−1−522−1+52−1−52-2-2−1+52−1−52−1+52−1−52001−521+521−521+520000
χ11222−1−52−1+522−1−52−1+5222−1−52−1+52−1−52−1+5200−1−52−1+52−1−52−1+520000
χ12222−1−52−1+522−1−52−1+52-2-2−1−52−1+52−1−52−1+52001+521−521+521−520000
χ1322-122-12200-1-1-1-1220000-1-100
χ1422-122-12200-1-1-1-1-2-200001100
χ152-22−1+52−1−52-21−521+522i−2i−1+52−1−521−521+5200−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000
χ162-22−1+52−1−52-21−521+52−2i2i−1+52−1−521−521+5200ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000
χ172-22−1−52−1+52-21+521−522i−2i−1−52−1+521+521−5200−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000
χ182-22−1−52−1+52-21+521−52−2i2i−1−52−1+521+521−5200ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000
χ192-2-1221-2-200-1-1112i−2i0000−ii00
χ202-2-1221-2-200-1-111−2i2i0000i−i00
χ2144-2−1+5−1−5-2−1+5−1−5001−521+521−521+520000000000
χ2244-2−1−5−1+5-2−1−5−1+5001+521−521+521−520000000000
χ234-4-2−1+5−1−521−51+5001−521+52−1+52−1−520000000000
χ244-4-2−1−5−1+521+51−5001+521−52−1−52−1+520000000000

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