Finite Group Databasebeta

← Group #13060780

Character table — Group #13060780

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85
size111122222233333333666666666666666666666666661212121212121212121212121212121212121212122828282828282828565656565656565656565656
order122222444477141414141414441414141428282828282828282828282828282828282828282441414141414142828282828282828282828283366666666661212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111−1−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
χ311111111111111111111111111111111111111111111111111111111111111111−1+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
χ4111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ5111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ6111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ71111-1-111-1-11111111111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ81111-1-111-1-11111111111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ91111-1-111-1-11111111111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ132-22-22-22i−2i2i−2i22-2-222-2-20022-2-22i2i−2i−2i0000000000002i2i−2i−2i000000000000000000000-1-1-1-111111-11-1i−ii−ii−ii−i
χ142-22-22-22i−2i2i−2i22-2-222-2-20022-2-22i2i−2i−2i0000000000002i2i−2i−2i0000000000000000000001+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ152-22-22-22i−2i2i−2i22-2-222-2-20022-2-22i2i−2i−2i0000000000002i2i−2i−2i0000000000000000000001−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ162-22-22-2−2i2i−2i2i22-2-222-2-20022-2-2−2i−2i2i2i000000000000−2i−2i2i2i000000000000000000000-1-1-1-111111-11-1−ii−ii−ii−ii
χ172-22-22-2−2i2i−2i2i22-2-222-2-20022-2-2−2i−2i2i2i000000000000−2i−2i2i2i0000000000000000000001+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ182-22-22-2−2i2i−2i2i22-2-222-2-20022-2-2−2i−2i2i2i000000000000−2i−2i2i2i0000000000000000000001−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ192-22-2-222i−2i−2i2i22-2-222-2-200-2-2222i2i−2i−2i000000000000−2i−2i2i2i000000000000000000000-1-1-1-11111-11-11i−i−iii−i−ii
χ202-22-2-222i−2i−2i2i22-2-222-2-200-2-2222i2i−2i−2i000000000000−2i−2i2i2i0000000000000000000001+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ212-22-2-222i−2i−2i2i22-2-222-2-200-2-2222i2i−2i−2i000000000000−2i−2i2i2i0000000000000000000001−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ222-22-2-22−2i2i2i−2i22-2-222-2-200-2-222−2i−2i2i2i0000000000002i2i−2i−2i000000000000000000000-1-1-1-11111-11-11−iii−i−iii−i
χ232-22-2-22−2i2i2i−2i22-2-222-2-200-2-222−2i−2i2i2i0000000000002i2i−2i−2i0000000000000000000001+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ242-22-2-22−2i2i2i−2i22-2-222-2-200-2-222−2i−2i2i2i0000000000002i2i−2i−2i0000000000000000000001−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ252-2-2200000022-2-2-2-2222-200000000222222-2-2-2-2-2-2000000000000000000000000022-2-22-22-2000000000000
χ262-2-2200000022-2-2-2-2222-200000000222222-2-2-2-2-2-20000000000000000000000000−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3000000000000
χ272-2-2200000022-2-2-2-2222-200000000222222-2-2-2-2-2-20000000000000000000000000−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3000000000000
χ28333333333333333333-1-133333333-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ293333333333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i7233−1−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−i72−1−i72−1+i72−1+i72−1+i72−1−i72−1+i72−1−i72−1+i72333−1−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+i72−1+i72−1+i7200000000000000000000
χ303333333333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72-1-1−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−1−i72−1+i72−1−i72−1+i72-1-1-1ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ8200000000000000000000
χ313333333333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72-1-1−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−1−i72−1+i72−1−i72−1+i72-1-1-1−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ8200000000000000000000
χ323333333333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72-1-1−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82−1−i72−1+i72−1−i72−1+i72-1-1-1−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ82−ζ2+ζ22−ζ46+ζ50−ζ58−ζ74ζ2−ζ22−ζ46−ζ50+ζ58−ζ74−ζ2−ζ22+ζ46−ζ50−ζ58+ζ74ζ10−ζ26−ζ34+ζ38−ζ62−ζ82−ζ10−ζ26+ζ34−ζ38+ζ62−ζ82−ζ10+ζ26−ζ34−ζ38−ζ62+ζ8200000000000000000000
χ333333333333−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i7233−1+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+i72−1+i72−1−i72−1−i72−1−i72−1+i72−1−i72−1+i72−1−i72333−1+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−i72−1−i72−1−i7200000000000000000000
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χ836-6-66000000−1+i7−1−i71−i71+i71−i71+i7−1+i7−1−i7-22000000002ζ10−2ζ26−2ζ34+2ζ38−2ζ62−2ζ82−2ζ10−2ζ26+2ζ34−2ζ38+2ζ62−2ζ82−2ζ10+2ζ26−2ζ34−2ζ38−2ζ62+2ζ822ζ2−2ζ22−2ζ46−2ζ50+2ζ58−2ζ74−2ζ2−2ζ22+2ζ46−2ζ50−2ζ58+2ζ74−2ζ2+2ζ22−2ζ46+2ζ50−2ζ58−2ζ74−2ζ10+2ζ26+2ζ34−2ζ38+2ζ62+2ζ822ζ10+2ζ26−2ζ34+2ζ38−2ζ62+2ζ822ζ10−2ζ26+2ζ34+2ζ38+2ζ62−2ζ82−2ζ2+2ζ22+2ζ46+2ζ50−2ζ58+2ζ742ζ2+2ζ22−2ζ46+2ζ50+2ζ58−2ζ742ζ2−2ζ22+2ζ46−2ζ50+2ζ58+2ζ74000000000000000000000000000000000000000000000
χ841212-12-12000000−2−2i7−2+2i7−2−2i7−2+2i72+2i72−2i72+2i72−2i70000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-12000000−2+2i7−2−2i7−2+2i7−2−2i72−2i72+2i72−2i72+2i70000000000000000000000000000000000000000000000000000000000000000000

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