Finite Group Databasebeta

← Group #4247

Character table — Group #4247

Order 168.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27
size1122222222444444666666614141442
order12367771414142121214242422141414141414412122
χ1111111111111111111111111111
χ211111111111111111111111-1-1-1-1
χ31111111111111111-1-1-1-1-1-1-1111-1
χ41111111111111111-1-1-1-1-1-1-1-1-1-11
χ52222ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ742ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ740000
χ62222ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74-2−ζ2−ζ26−ζ58−ζ82−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ10−ζ38−ζ46−ζ740000
χ72222ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ822ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ820000
χ82222ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82-2−ζ22−ζ34−ζ50−ζ62−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ2−ζ26−ζ58−ζ820000
χ92222ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ622ζ10+ζ38+ζ46+ζ74ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ22+ζ34+ζ50+ζ620000
χ102222ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62-2−ζ10−ζ38−ζ46−ζ74−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ22−ζ34−ζ50−ζ620000
χ1122-1-1222222-1-1-1-1-1-100000002-1-10
χ1222-1-1222222-1-1-1-1-1-10000000-2110
χ132-22-2222-2-2-2222-2-2-200000000000
χ142-22-2ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ740ζ2−ζ26+ζ58−ζ82−ζ2+ζ26−ζ58+ζ82ζ22−ζ34+ζ50−ζ62−ζ22+ζ34−ζ50+ζ62−ζ10−ζ38+ζ46+ζ74ζ10+ζ38−ζ46−ζ740000
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+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ740−ζ2+ζ26−ζ58+ζ82ζ2−ζ26+ζ58−ζ82−ζ22+ζ34−ζ50+ζ62ζ22−ζ34+ζ50−ζ62ζ10+ζ38−ζ46−ζ74−ζ10−ζ38+ζ46+ζ740000
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+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ820ζ22−ζ34+ζ50−ζ62−ζ22+ζ34−ζ50+ζ62−ζ10−ζ38+ζ46+ζ74ζ10+ζ38−ζ46−ζ74ζ2−ζ26+ζ58−ζ82−ζ2+ζ26−ζ58+ζ820000
χ172-22-2ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ820−ζ22+ζ34−ζ50+ζ62ζ22−ζ34+ζ50−ζ62ζ10+ζ38−ζ46−ζ74−ζ10−ζ38+ζ46+ζ74−ζ2+ζ26−ζ58+ζ82ζ2−ζ26+ζ58−ζ820000
χ182-22-2ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ620−ζ10−ζ38+ζ46+ζ74ζ10+ζ38−ζ46−ζ74ζ2−ζ26+ζ58−ζ82−ζ2+ζ26−ζ58+ζ82ζ22−ζ34+ζ50−ζ62−ζ22+ζ34−ζ50+ζ620000
χ192-22-2ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ620ζ10+ζ38−ζ46−ζ74−ζ10−ζ38+ζ46+ζ74−ζ2+ζ26−ζ58+ζ82ζ2−ζ26+ζ58−ζ82−ζ22+ζ34−ζ50+ζ62ζ22−ζ34+ζ50−ζ620000
χ202-2-11222-2-2-2-1-1-1111000000003−30
χ212-2-11222-2-2-2-1-1-111100000000−330
χ2244-2-22ζ2+2ζ26+2ζ58+2ζ822ζ22+2ζ34+2ζ50+2ζ622ζ10+2ζ38+2ζ46+2ζ742ζ2+2ζ26+2ζ58+2ζ822ζ22+2ζ34+2ζ50+2ζ622ζ10+2ζ38+2ζ46+2ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ7400000000000
χ2344-2-22ζ22+2ζ34+2ζ50+2ζ622ζ10+2ζ38+2ζ46+2ζ742ζ2+2ζ26+2ζ58+2ζ822ζ22+2ζ34+2ζ50+2ζ622ζ10+2ζ38+2ζ46+2ζ742ζ2+2ζ26+2ζ58+2ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ8200000000000
χ2444-2-22ζ10+2ζ38+2ζ46+2ζ742ζ2+2ζ26+2ζ58+2ζ822ζ22+2ζ34+2ζ50+2ζ622ζ10+2ζ38+2ζ46+2ζ742ζ2+2ζ26+2ζ58+2ζ822ζ22+2ζ34+2ζ50+2ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ6200000000000
χ254-4-222ζ2+2ζ26+2ζ58+2ζ822ζ22+2ζ34+2ζ50+2ζ622ζ10+2ζ38+2ζ46+2ζ74−2ζ2−2ζ26−2ζ58−2ζ82−2ζ22−2ζ34−2ζ50−2ζ62−2ζ10−2ζ38−2ζ46−2ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ7400000000000
χ264-4-222ζ22+2ζ34+2ζ50+2ζ622ζ10+2ζ38+2ζ46+2ζ742ζ2+2ζ26+2ζ58+2ζ82−2ζ22−2ζ34−2ζ50−2ζ62−2ζ10−2ζ38−2ζ46−2ζ74−2ζ2−2ζ26−2ζ58−2ζ82−ζ22−ζ34−ζ50−ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82ζ22+ζ34+ζ50+ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ8200000000000
χ274-4-222ζ10+2ζ38+2ζ46+2ζ742ζ2+2ζ26+2ζ58+2ζ822ζ22+2ζ34+2ζ50+2ζ62−2ζ10−2ζ38−2ζ46−2ζ74−2ζ2−2ζ26−2ζ58−2ζ82−2ζ22−2ζ34−2ζ50−2ζ62−ζ10−ζ38−ζ46−ζ74−ζ2−ζ26−ζ58−ζ82−ζ22−ζ34−ζ50−ζ62ζ10+ζ38+ζ46+ζ74ζ2+ζ26+ζ58+ζ82ζ22+ζ34+ζ50+ζ6200000000000

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