Finite Group Databasebeta

← Group #6764

Character table — Group #6764

Order 240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size11222226622444441212224444412125510101010103030
order12346121244510152030606020205101520306060202022646121244
χ1111111111111111111111111111111111111
χ21111111-1-11111111-1-11111111-1-11111111-1-1
χ3111-11-1-11-1111-11-1-11-1111-11-1-11-1111-11-1-11-1
χ4111-11-1-1-11111-11-1-1-11111-11-1-1-11111-11-1-1-11
χ522-12-1-1-10022-12-1-1-10022-12-1-1-10022-12-1-1-100
χ622-1-2-1110022-1-2-1110022-1-2-1110022-1-2-11100
χ72-220-200002-220-200002-220-200002-220-20000
χ82-2-1013−3002-2-1013−3002-2-1013−3002-2-1013−300
χ92-2-101−33002-2-101−33002-2-101−33002-2-101−3300
χ10111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ111111111-1-11111111-1-11111111-1-1-1-1-1-1-1-1-111
χ12111-11-1-11-1111-11-1-11-1111-11-1-11-1-1-1-11-111-11
χ13111-11-1-1-11111-11-1-1-11111-11-1-1-11-1-1-11-1111-1
χ1422-12-1-1-10022-12-1-1-10022-12-1-1-100-2-21-211100
χ1522-1-2-1110022-1-2-1110022-1-2-11100-2-2121-1-100
χ162-220-200002-220-200002-220-20000-22-2020000
χ172-2-1013−3002-2-1013−3002-2-1013−300-2210-1−3300
χ182-2-101−33002-2-101−33002-2-101−3300-2210-13−300
χ19222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52000000000
χ202222222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52000000000
χ21222-22-2-22-2−1+52−1+52−1+521−52−1+521−521−52−1+521−52−1−52−1−52−1−521+52−1−521+521+52−1−521+52000000000
χ22222-22-2-2-22−1+52−1+52−1+521−52−1+521−521−521−52−1+52−1−52−1−52−1−521+52−1−521+521+521+52−1−52000000000
χ2344-24-2-2-200−1+5−1+51−52−1+51−521−521−5200−1−5−1−51+52−1−51+521+521+5200000000000
χ2444-2-4-22200−1+5−1+51−521−51−52−1+52−1+5200−1−5−1−51+521+51+52−1−52−1−5200000000000
χ254-440-40000−1+51−5−1+501−50000−1−51+5−1−501+50000000000000
χ264-4-20223−2300−1+51−51−520−1+52ζ7−ζ23+ζ43−ζ47−ζ7+ζ23−ζ43+ζ4700−1−51+51+520−1−52−ζ11+ζ19+ζ31−ζ59ζ11−ζ19−ζ31+ζ5900000000000
χ274-4-202−232300−1+51−51−520−1+52−ζ7+ζ23−ζ43+ζ47ζ7−ζ23+ζ43−ζ4700−1−51+51+520−1−52ζ11−ζ19−ζ31+ζ59−ζ11+ζ19+ζ31−ζ5900000000000
χ28222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52000000000
χ292222222-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52000000000
χ30222-22-2-22-2−1−52−1−52−1−521+52−1−521+521+52−1−521+52−1+52−1+52−1+521−52−1+521−521−52−1+521−52000000000
χ31222-22-2-2-22−1−52−1−52−1−521+52−1−521+521+521+52−1−52−1+52−1+52−1+521−52−1+521−521−521−52−1+52000000000
χ3244-24-2-2-200−1−5−1−51+52−1−51+521+521+5200−1+5−1+51−52−1+51−521−521−5200000000000
χ3344-2-4-22200−1−5−1−51+521+51+52−1−52−1−5200−1+5−1+51−521−51−52−1+52−1+5200000000000
χ344-440-40000−1−51+5−1−501+50000−1+51−5−1+501−50000000000000
χ354-4-20223−2300−1−51+51+520−1−52−ζ11+ζ19+ζ31−ζ59ζ11−ζ19−ζ31+ζ5900−1+51−51−520−1+52ζ7−ζ23+ζ43−ζ47−ζ7+ζ23−ζ43+ζ4700000000000
χ364-4-202−232300−1−51+51+520−1−52ζ11−ζ19−ζ31+ζ59−ζ11+ζ19+ζ31−ζ5900−1+51−51−520−1+52−ζ7+ζ23−ζ43+ζ47ζ7−ζ23+ζ43−ζ4700000000000

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