Finite Group Databasebeta

← Group #6749

Character table — Group #6749

Order 240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size11222255336666151544888820204488882020
order12551010442210101010443615153030121236151530301212
χ111111111111111111111111111111111
χ2111111-1-1111111-1-1111111-1-1111111-1-1
χ31-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i
χ41-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii
χ522−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200
χ622−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200
χ72-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200
χ82-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200
χ91111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ10111111-1-1111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ111-111-1-1i−i1-111-1-1i−i−1+i321−i32−1+i32−1+i321−i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59−1−i321+i32−1−i32−1−i321+i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43
χ121-111-1-1−ii1-111-1-1−ii−1+i321−i32−1+i32−1+i321−i321−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59−1−i321+i32−1−i32−1−i321+i321+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43
χ1322−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200−1+i3−1+i3−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ2600−1−i3−1−i3−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ4600
χ1422−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200−1+i3−1+i3−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ3800−1−i3−1−i3−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ5800
χ152-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200−1+i31−i3−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ14+ζ2600−1−i31+i3−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ34+ζ4600
χ162-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200−1+i31−i3−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ2+ζ3800−1−i31+i3−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ22+ζ5800
χ171111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ18111111-1-1111111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ191-111-1-1i−i1-111-1-1i−i−1−i321+i32−1−i32−1−i321+i321+i32−ζ7−ζ19−ζ31−ζ43ζ7+ζ19+ζ31+ζ43−1+i321−i32−1+i32−1+i321−i321−i32−ζ11−ζ23−ζ47−ζ59ζ11+ζ23+ζ47+ζ59
χ201-111-1-1−ii1-111-1-1−ii−1−i321+i32−1−i32−1−i321+i321+i32ζ7+ζ19+ζ31+ζ43−ζ7−ζ19−ζ31−ζ43−1+i321−i32−1+i32−1+i321−i321−i32ζ11+ζ23+ζ47+ζ59−ζ11−ζ23−ζ47−ζ59
χ2122−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200−1−i3−1−i3−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ4600−1+i3−1+i3−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ2600
χ2222−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200−1−i3−1−i3−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ5800−1+i3−1+i3−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ3800
χ232-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200−1−i31+i3−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ34+ζ4600−1+i31−i3−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ14+ζ2600
χ242-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200−1−i31+i3−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ22+ζ5800−1+i31−i3−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ2+ζ3800
χ2533333333-1-1-1-1-1-1-1-10000000000000000
χ26333333-3-3-1-1-1-1-1-1110000000000000000
χ273-333-3-33i−3i-11-1-111−ii0000000000000000
χ283-333-3-3−3i3i-11-1-111i−i0000000000000000
χ2966−3+352−3−352−3+352−3−35200-2-21−521+521−521+52000000000000000000
χ3066−3−352−3+352−3−352−3+35200-2-21+521−521+521−52000000000000000000
χ316-6−3+352−3−3523−3523+35200-221−521+52−1+52−1−52000000000000000000
χ326-6−3−352−3+3523+3523−35200-221+521−52−1−52−1+52000000000000000000

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