Finite Group Databasebeta

← Group #746

Character table — Group #746

Order 84.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24
size11222222222222222222222121
order123677714141421212121212142424242424244
χ1111111111111111111111111
χ21111111111111111111111-1-1
χ31-11-1111-1-1-1111111-1-1-1-1-1-1i−i
χ41-11-1111-1-1-1111111-1-1-1-1-1-1−ii
χ52222ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ7400
χ62222ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ8200
χ72222ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ6200
χ822-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100
χ922-1-1ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ2−ζ82−ζ26−ζ58−ζ22−ζ62−ζ34−ζ50−ζ10−ζ74−ζ38−ζ46−ζ2−ζ82−ζ26−ζ58−ζ22−ζ62−ζ34−ζ50−ζ10−ζ74−ζ38−ζ4600
χ1022-1-1ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ26−ζ58−ζ2−ζ82−ζ34−ζ50−ζ22−ζ62−ζ38−ζ46−ζ10−ζ74−ζ26−ζ58−ζ2−ζ82−ζ34−ζ50−ζ22−ζ62−ζ38−ζ46−ζ10−ζ7400
χ1122-1-1ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ22−ζ62−ζ34−ζ50−ζ10−ζ74−ζ38−ζ46−ζ26−ζ58−ζ2−ζ82−ζ22−ζ62−ζ34−ζ50−ζ10−ζ74−ζ38−ζ46−ζ26−ζ58−ζ2−ζ8200
χ1222-1-1ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ34−ζ50−ζ22−ζ62−ζ38−ζ46−ζ10−ζ74−ζ2−ζ82−ζ26−ζ58−ζ34−ζ50−ζ22−ζ62−ζ38−ζ46−ζ10−ζ74−ζ2−ζ82−ζ26−ζ5800
χ1322-1-1ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ74−ζ38−ζ46−ζ26−ζ58−ζ2−ζ82−ζ34−ζ50−ζ22−ζ62−ζ10−ζ74−ζ38−ζ46−ζ26−ζ58−ζ2−ζ82−ζ34−ζ50−ζ22−ζ6200
χ1422-1-1ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ38−ζ46−ζ10−ζ74−ζ2−ζ82−ζ26−ζ58−ζ22−ζ62−ζ34−ζ50−ζ38−ζ46−ζ10−ζ74−ζ2−ζ82−ζ26−ζ58−ζ22−ζ62−ζ34−ζ5000
χ152-22-2ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74−ζ2−ζ26−ζ58−ζ82−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ10−ζ38−ζ46−ζ7400
χ162-22-2ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82−ζ22−ζ34−ζ50−ζ62−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ2−ζ26−ζ58−ζ8200
χ172-22-2ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ22−ζ34−ζ50−ζ6200
χ182-2-11222-2-2-2-1-1-1-1-1-111111100
χ192-2-11ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ82−ζ26−ζ58−ζ22−ζ62−ζ34−ζ50−ζ10−ζ74−ζ38−ζ46ζ2+ζ82ζ26+ζ58ζ22+ζ62ζ34+ζ50ζ10+ζ74ζ38+ζ4600
χ202-2-11ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ26−ζ58−ζ2−ζ82−ζ34−ζ50−ζ22−ζ62−ζ38−ζ46−ζ10−ζ74ζ26+ζ58ζ2+ζ82ζ34+ζ50ζ22+ζ62ζ38+ζ46ζ10+ζ7400
χ212-2-11ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ62−ζ34−ζ50−ζ10−ζ74−ζ38−ζ46−ζ26−ζ58−ζ2−ζ82ζ22+ζ62ζ34+ζ50ζ10+ζ74ζ38+ζ46ζ26+ζ58ζ2+ζ8200
χ222-2-11ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ34−ζ50−ζ22−ζ62−ζ38−ζ46−ζ10−ζ74−ζ2−ζ82−ζ26−ζ58ζ34+ζ50ζ22+ζ62ζ38+ζ46ζ10+ζ74ζ2+ζ82ζ26+ζ5800
χ232-2-11ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ74−ζ38−ζ46−ζ26−ζ58−ζ2−ζ82−ζ34−ζ50−ζ22−ζ62ζ10+ζ74ζ38+ζ46ζ26+ζ58ζ2+ζ82ζ34+ζ50ζ22+ζ6200
χ242-2-11ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ38−ζ46−ζ10−ζ74−ζ2−ζ82−ζ26−ζ58−ζ22−ζ62−ζ34−ζ50ζ38+ζ46ζ10+ζ74ζ2+ζ82ζ26+ζ58ζ22+ζ62ζ34+ζ5000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.