Finite Group Databasebeta

← Group #11759071

Character table — Group #11759071

Order 1008.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1333331616399999484839999948487212121212111211272121212121112112
order12444433714282828282121714282828282121361212121233361212121233
χ11111111111111111111111111111111111111111
χ2111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32
χ3111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32
χ433-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-100
χ53-111−1+2i−1−2i003-111−1+2i−1−2i003-111−1+2i−1−2i003-111−1+2i−1−2i003-111−1+2i−1−2i00
χ63-111−1−2i−1+2i003-111−1−2i−1+2i003-111−1−2i−1+2i003-111−1−2i−1+2i003-111−1−2i−1+2i00
χ73-1−1+2i−1−2i11003-1−1+2i−1−2i11003-1−1+2i−1−2i11003-1−1+2i−1−2i11003-1−1+2i−1−2i1100
χ83-1−1−2i−1+2i11003-1−1−2i−1+2i11003-1−1−2i−1+2i11003-1−1−2i−1+2i11003-1−1−2i−1+2i1100
χ9111111111111111111111111−1+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−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321
χ11111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32
χ1233-1-1-1-10033-1-1-1-10033-1-1-1-100−3+3i32−3+3i321−i321−i321−i321−i3200−3−3i32−3−3i321+i321+i321+i321+i3200
χ133-111−1+2i−1−2i003-111−1+2i−1−2i003-111−1+2i−1−2i00−3+3i321−i32−1+i32−1+i32−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ82−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ8200−3−3i321+i32−1−i32−1−i32−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ83−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ8300
χ143-111−1−2i−1+2i003-111−1−2i−1+2i003-111−1−2i−1+2i00−3+3i321−i32−1+i32−1+i32−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ82−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ8200−3−3i321+i32−1−i32−1−i32−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ83−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ8300
χ153-1−1+2i−1−2i11003-1−1+2i−1−2i11003-1−1+2i−1−2i1100−3+3i321−i32−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ82−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ82−1+i32−1+i3200−3−3i321+i32−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ83−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ83−1−i32−1−i3200
χ163-1−1−2i−1+2i11003-1−1−2i−1+2i11003-1−1−2i−1+2i1100−3+3i321−i32−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ82−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ82−1+i32−1+i3200−3−3i321+i32−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ83−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ83−1−i32−1−i3200
χ17111111111111111111111111−1−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−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32
χ19111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321
χ2033-1-1-1-10033-1-1-1-10033-1-1-1-100−3−3i32−3−3i321+i321+i321+i321+i3200−3+3i32−3+3i321−i321−i321−i321−i3200
χ213-111−1+2i−1−2i003-111−1+2i−1−2i003-111−1+2i−1−2i00−3−3i321+i32−1−i32−1−i32−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ83−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ8300−3+3i321−i32−1+i32−1+i32−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ82−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ8200
χ223-111−1−2i−1+2i003-111−1−2i−1+2i003-111−1−2i−1+2i00−3−3i321+i32−1−i32−1−i32−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ83−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ8300−3+3i321−i32−1+i32−1+i32−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ82−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ8200
χ233-1−1+2i−1−2i11003-1−1+2i−1−2i11003-1−1+2i−1−2i1100−3−3i321+i32−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ83−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ83−1−i32−1−i3200−3+3i321−i32−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ82−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ82−1+i32−1+i3200
χ243-1−1−2i−1+2i11003-1−1−2i−1+2i11003-1−1−2i−1+2i1100−3−3i321+i32−ζ2−2ζ11−2ζ23−ζ26−ζ38−2ζ47−ζ50−2ζ59−ζ62−2ζ71−ζ74−2ζ83−ζ2+2ζ11+2ζ23−ζ26−ζ38+2ζ47−ζ50+2ζ59−ζ62+2ζ71−ζ74+2ζ83−1−i32−1−i3200−3+3i321−i32−ζ10−2ζ19−ζ22−2ζ31−ζ34−2ζ43−ζ46−2ζ55−ζ58−2ζ67−2ζ79−ζ82−ζ10+2ζ19−ζ22+2ζ31−ζ34+2ζ43−ζ46+2ζ55−ζ58+2ζ67+2ζ79−ζ82−1+i32−1+i3200
χ2533333333−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−1+i720000000000000000
χ26333333−3−3i32−3+3i32−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−ζ2−ζ50−ζ74−ζ22−ζ46−ζ58−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−ζ26−ζ38−ζ62−ζ10−ζ34−ζ820000000000000000
χ27333333−3+3i32−3−3i32−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−ζ22−ζ46−ζ58−ζ2−ζ50−ζ74−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−ζ10−ζ34−ζ82−ζ26−ζ38−ζ620000000000000000
χ2899-3-3-3-300−3−3i72−3−3i721+i721+i721+i721+i7200−3+3i72−3+3i721−i721−i721−i721−i72000000000000000000
χ299-333−3+6i−3−6i00−3−3i721+i72−1−i72−1−i72−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ79−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ7900−3+3i721−i72−1+i72−1+i72−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ83−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ83000000000000000000
χ309-333−3−6i−3+6i00−3−3i721+i72−1−i72−1−i72−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ79−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ7900−3+3i721−i72−1+i72−1+i72−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ83−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ83000000000000000000
χ319-3−3+6i−3−6i3300−3−3i721+i72−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ79−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ79−1−i72−1−i7200−3+3i721−i72−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ83−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ83−1+i72−1+i72000000000000000000
χ329-3−3−6i−3+6i3300−3−3i721+i72−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ79−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ79−1−i72−1−i7200−3+3i721−i72−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ83−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ83−1+i72−1+i72000000000000000000
χ3333333333−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−1−i720000000000000000
χ34333333−3−3i32−3+3i32−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−ζ26−ζ38−ζ62−ζ10−ζ34−ζ82−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−ζ2−ζ50−ζ74−ζ22−ζ46−ζ580000000000000000
χ35333333−3+3i32−3−3i32−1+i72−1+i72−1+i72−1+i72−1+i72−1+i72−ζ10−ζ34−ζ82−ζ26−ζ38−ζ62−1−i72−1−i72−1−i72−1−i72−1−i72−1−i72−ζ22−ζ46−ζ58−ζ2−ζ50−ζ740000000000000000
χ3699-3-3-3-300−3+3i72−3+3i721−i721−i721−i721−i7200−3−3i72−3−3i721+i721+i721+i721+i72000000000000000000
χ379-333−3+6i−3−6i00−3+3i721−i72−1+i72−1+i72−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ83−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ8300−3−3i721+i72−1−i72−1−i72−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ79−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ79000000000000000000
χ389-333−3−6i−3+6i00−3+3i721−i72−1+i72−1+i72−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ83−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ8300−3−3i721+i72−1−i72−1−i72−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ79−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ79000000000000000000
χ399-3−3+6i−3−6i3300−3+3i721−i72−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ83−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ83−1+i72−1+i7200−3−3i721+i72−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ79−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ79−1−i72−1−i72000000000000000000
χ409-3−3−6i−3+6i3300−3+3i721−i72−ζ10−2ζ19−ζ26−2ζ31−ζ34−ζ38−2ζ47−2ζ55−2ζ59−ζ62−ζ82−2ζ83−ζ10+2ζ19−ζ26+2ζ31−ζ34−ζ38+2ζ47+2ζ55+2ζ59−ζ62−ζ82+2ζ83−1+i72−1+i7200−3−3i721+i72−ζ2−2ζ11−ζ22−2ζ23−2ζ43−ζ46−ζ50−ζ58−2ζ67−2ζ71−ζ74−2ζ79−ζ2+2ζ11−ζ22+2ζ23+2ζ43−ζ46−ζ50−ζ58+2ζ67+2ζ71−ζ74+2ζ79−1−i72−1−i72000000000000000000

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