Finite Group Databasebeta

← Group #1206

Character table — Group #1206

Order 120.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39
size112222222221010112222222221010112222222221010
order1245510102020202044361215153030606060601212361215153030606060601212
χ1111111111111111111111111111111111111111
χ211111111111-1-111111111111-1-111111111111-1-1
χ311-11111-1-1-1-11-111-11111-1-1-1-11-111-11111-1-1-1-11-1
χ411-11111-1-1-1-1-1111-11111-1-1-1-1-1111-11111-1-1-1-1-11
χ5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200
χ6222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200
χ722-2−1+52−1−52−1+52−1−521−521−521+521+520022-2−1+52−1−52−1+52−1−521−521−521+521+520022-2−1+52−1−52−1+52−1−521−521−521+521+5200
χ822-2−1−52−1+52−1−52−1+521+521+521−521−520022-2−1−52−1+52−1−52−1+521+521+521−521−520022-2−1−52−1+52−1−52−1+521+521+521−521−5200
χ92-2022-2-20000002-2022-2-20000002-2022-2-2000000
χ102-20−1+52−1−521−521+52ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59002-20−1+52−1−521−521+52ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59002-20−1+52−1−521−521+52ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ5900
χ112-20−1+52−1−521−521+52−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59002-20−1+52−1−521−521+52−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59002-20−1+52−1−521−521+52−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ5900
χ122-20−1−52−1+521+521−52−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47002-20−1−52−1+521+521−52−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47002-20−1−52−1+521+521−52−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ4700
χ132-20−1−52−1+521+521−52ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47002-20−1−52−1+521+521−52ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47002-20−1−52−1+521+521−52ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ4700
χ141111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ1511111111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ1611-11111-1-1-1-11-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32
χ1711-11111-1-1-1-1-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32
χ18222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200−1+i3−1+i3−1+i3−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ2−ζ38−ζ14−ζ26−ζ14−ζ2600−1−i3−1−i3−1−i3−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ22−ζ58−ζ34−ζ46−ζ34−ζ4600
χ19222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200−1+i3−1+i3−1+i3−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ14−ζ26−ζ2−ζ38−ζ2−ζ3800−1−i3−1−i3−1−i3−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ34−ζ46−ζ22−ζ58−ζ22−ζ5800
χ2022-2−1+52−1−52−1+52−1−521−521−521+521+5200−1+i3−1+i31−i3−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ2+ζ38ζ14+ζ26ζ14+ζ2600−1−i3−1−i31+i3−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ22+ζ58ζ34+ζ46ζ34+ζ4600
χ2122-2−1−52−1+52−1−52−1+521+521+521−521−5200−1+i3−1+i31−i3−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ14+ζ26ζ2+ζ38ζ2+ζ3800−1−i3−1−i31+i3−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ34+ζ46ζ22+ζ58ζ22+ζ5800
χ222-2022-2-2000000−1+i31−i30−1+i3−1+i31−i31−i3000000−1−i31+i30−1−i3−1−i31+i31+i3000000
χ232-20−1+52−1−521−521+52ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ5900−1+i31−i30−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ14+ζ26ζ23−ζ47−ζ23+ζ47ζ11−ζ59−ζ11+ζ5900−1−i31+i30−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ34+ζ46−ζ7+ζ43ζ7−ζ43−ζ19+ζ31ζ19−ζ3100
χ242-20−1+52−1−521−521+52−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ5900−1+i31−i30−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ14+ζ26−ζ23+ζ47ζ23−ζ47−ζ11+ζ59ζ11−ζ5900−1−i31+i30−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ34+ζ46ζ7−ζ43−ζ7+ζ43ζ19−ζ31−ζ19+ζ3100
χ252-20−1−52−1+521+521−52−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ4700−1+i31−i30−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ2+ζ38ζ11−ζ59−ζ11+ζ59−ζ23+ζ47ζ23−ζ4700−1−i31+i30−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ22+ζ58−ζ19+ζ31ζ19−ζ31ζ7−ζ43−ζ7+ζ4300
χ262-20−1−52−1+521+521−52ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ4700−1+i31−i30−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ2+ζ38−ζ11+ζ59ζ11−ζ59ζ23−ζ47−ζ23+ζ4700−1−i31+i30−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ22+ζ58ζ19−ζ31−ζ19+ζ31−ζ7+ζ43ζ7−ζ4300
χ271111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ2811111111111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ2911-11111-1-1-1-11-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32
χ3011-11111-1-1-1-1-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32
χ31222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5200−1−i3−1−i3−1−i3−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ22−ζ58−ζ34−ζ46−ζ34−ζ4600−1+i3−1+i3−1+i3−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ2−ζ38−ζ14−ζ26−ζ14−ζ2600
χ32222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5200−1−i3−1−i3−1−i3−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ34−ζ46−ζ22−ζ58−ζ22−ζ5800−1+i3−1+i3−1+i3−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ14−ζ26−ζ2−ζ38−ζ2−ζ3800
χ3322-2−1+52−1−52−1+52−1−521−521−521+521+5200−1−i3−1−i31+i3−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ22+ζ58ζ34+ζ46ζ34+ζ4600−1+i3−1+i31−i3−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ2+ζ38ζ14+ζ26ζ14+ζ2600
χ3422-2−1−52−1+52−1−52−1+521+521+521−521−5200−1−i3−1−i31+i3−ζ34−ζ46−ζ22−ζ58−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ34+ζ46ζ22+ζ58ζ22+ζ5800−1+i3−1+i31−i3−ζ14−ζ26−ζ2−ζ38−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ14+ζ26ζ2+ζ38ζ2+ζ3800
χ352-2022-2-2000000−1−i31+i30−1−i3−1−i31+i31+i3000000−1+i31−i30−1+i3−1+i31−i31−i3000000
χ362-20−1+52−1−521−521+52ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ47−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ5900−1−i31+i30−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ34+ζ46−ζ7+ζ43ζ7−ζ43−ζ19+ζ31ζ19−ζ3100−1+i31−i30−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ14+ζ26ζ23−ζ47−ζ23+ζ47ζ11−ζ59−ζ11+ζ5900
χ372-20−1+52−1−521−521+52−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ47ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ5900−1−i31+i30−ζ22−ζ58−ζ34−ζ46ζ22+ζ58ζ34+ζ46ζ7−ζ43−ζ7+ζ43ζ19−ζ31−ζ19+ζ3100−1+i31−i30−ζ2−ζ38−ζ14−ζ26ζ2+ζ38ζ14+ζ26−ζ23+ζ47ζ23−ζ47−ζ11+ζ59ζ11−ζ5900
χ382-20−1−52−1+521+521−52−ζ11+ζ19−ζ31+ζ59ζ11−ζ19+ζ31−ζ59−ζ7+ζ23+ζ43−ζ47ζ7−ζ23−ζ43+ζ4700−1−i31+i30−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ22+ζ58−ζ19+ζ31ζ19−ζ31ζ7−ζ43−ζ7+ζ4300−1+i31−i30−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ2+ζ38ζ11−ζ59−ζ11+ζ59−ζ23+ζ47ζ23−ζ4700
χ392-20−1−52−1+521+521−52ζ11−ζ19+ζ31−ζ59−ζ11+ζ19−ζ31+ζ59ζ7−ζ23−ζ43+ζ47−ζ7+ζ23+ζ43−ζ4700−1−i31+i30−ζ34−ζ46−ζ22−ζ58ζ34+ζ46ζ22+ζ58ζ19−ζ31−ζ19+ζ31−ζ7+ζ43ζ7−ζ4300−1+i31−i30−ζ14−ζ26−ζ2−ζ38ζ14+ζ26ζ2+ζ38−ζ11+ζ59ζ11−ζ59ζ23−ζ47−ζ23+ζ4700

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