Finite Group Databasebeta

← Group #72230265

Character table — Group #72230265

Order 2688.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11266666666666666121212121212121212121212121212121212121212121212121212121212141442424242424242424242112112112112224224224224224224
order12422222444447142828141414141414141414141414141414282828282828282828282828282828222222224444336666661212
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32
χ311111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32
χ611111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32
χ711-1111-1-111-1-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-111111-11-1-1-1
χ811-1111-1-111-1-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32
χ911-1111-1-111-1-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32
χ1011-1111-1-111-1-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1111111-11-11-1-1
χ1111-1111-1-111-1-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111−1−i32−1+i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32
χ1211-1111-1-111-1-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111−1+i32−1−i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32
χ133333-1-1-1-1-1-13-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1333-1-13-1-1-1-1-1-10000000000
χ143333-1-1-1-1-1-13-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-3-3-311-31111110000000000
χ15333-13-1-1-1-1-1-13-13333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-133-13-1-13-1-1-1-1-10000000000
χ16333-13-1-1-1-1-1-13-13333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-3-31-311-3111110000000000
χ17333-1-13-1-1-1-1-1-133333-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333-1-13-1-13-1-1-1-10000000000
χ18333-1-13-1-1-1-1-1-133333-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333-3-311-311-311110000000000
χ19333-1-1-13-13-1-1-1-13333-1-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-13-13-10000000000
χ20333-1-1-13-13-1-1-1-13333-1-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-3-3111111-31-310000000000
χ21333-1-1-1-13-13-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-13-130000000000
χ22333-1-1-1-13-13-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1333-1-1-1-1-1-1-1-1-1-3-31111111-31-30000000000
χ2333-33-1-111-1-1-31133-3-3333-1-1-1-1-1-1111111-1-1-1-1-1-1-3-3-31111113-33-1-1-311-1-1110000000000
χ2433-33-1-111-1-1-31133-3-3333-1-1-1-1-1-1111111-1-1-1-1-1-1-3-3-3111111-33-3113-1-111-1-10000000000
χ2533-3-13-111-1-11-3133-3-3-1-1-1333-1-1-1111111-1-1-1-1-1-1111-3-3-31113-3-13-11-31-1-1110000000000
χ2633-3-13-111-1-11-3133-3-3-1-1-1333-1-1-1111111-1-1-1-1-1-1111-3-3-3111-331-31-13-111-1-10000000000
χ2733-3-1-1311-1-111-333-3-3-1-1-1-1-1-1333111111-1-1-1-1-1-1111111-3-3-33-3-1-1311-3-1-1110000000000
χ2833-3-1-1311-1-111-333-3-3-1-1-1-1-1-1333111111-1-1-1-1-1-1111111-3-3-3-3311-3-1-1311-1-10000000000
χ2933-3-1-1-11-3-1311133-3-3-1-1-1-1-1-1-1-1-1111-3-3-3-1-1-13331111111113-3-1-1-1111-131-30000000000
χ3033-3-1-1-11-3-1311133-3-3-1-1-1-1-1-1-1-1-1111-3-3-3-1-1-1333111111111-33111-1-1-11-3-130000000000
χ3133-3-1-1-1-313-111133-3-3-1-1-1-1-1-1-1-1-1-3-3-3111333-1-1-11111111113-3-1-1-11113-1-310000000000
χ3233-3-1-1-1-313-111133-3-3-1-1-1-1-1-1-1-1-1-3-3-3111333-1-1-1111111111-33111-1-1-1-313-10000000000
χ336666666666666-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ346666-2-2-2-2-2-26-2-2-1-1-1-1-1-1-1ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82-1-1-1ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ820000000000000000000000
χ356666-2-2-2-2-2-26-2-2-1-1-1-1-1-1-1−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82-1-1-1−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ820000000000000000000000
χ366666-2-2-2-2-2-26-2-2-1-1-1-1-1-1-1−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82-1-1-1−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ82−ζ2+ζ10−ζ22−ζ26−ζ34+ζ38+ζ46−ζ50−ζ58−ζ62+ζ74−ζ82ζ2−ζ10−ζ22+ζ26−ζ34−ζ38−ζ46−ζ50+ζ58−ζ62−ζ74+ζ82−ζ2−ζ10+ζ22−ζ26+ζ34−ζ38−ζ46+ζ50−ζ58+ζ62−ζ74−ζ820000000000000000000000
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χ658-8000000000008-80000000000000000000000000000000000000000000022-2-2000000
χ668-8000000000008-800000000000000000000000000000000000000000000−1−i3−1+i31+i31−i3000000
χ678-8000000000008-800000000000000000000000000000000000000000000−1+i3−1−i31−i31+i3000000
χ6824-2400000000000-4447−470000000000000000000000000000000000000000000000000000
χ6924-2400000000000-44−47470000000000000000000000000000000000000000000000000000

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