Finite Group Databasebeta

← Group #242

Character table — Group #242

Order 48.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size111111111111111111111111111111111111111111111111
order1424312612312612242461261261261224246126126126122424612612612612
χ1111111111111111111111111111111111111111111111111
χ21i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i
χ31-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-1
χ41−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i
χ51111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ61i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ111i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ111i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ111i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ11
χ71-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ81−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ111−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ111−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ111−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ11
χ91111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ101i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ71i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ71i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ71i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ7
χ111-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ121−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ71−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ71−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ71−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ7
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ141i-1−i1i-1−i1i-1−i-1−i1i-1−i1i-1−i1i1i-1−i1i-1−i1i-1−i-1−i1i-1−i1i-1−i1i
χ151-11-11-11-11-11-1-11-11-11-11-11-111-11-11-11-11-11-1-11-11-11-11-11-11
χ161−i-1i1−i-1i1−i-1i-1i1−i-1i1−i-1i1−i1−i-1i1−i-1i1−i-1i-1i1−i-1i1−i-1i1−i
χ171111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32
χ181i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ11-1−i1i1−i32−ζ7−1+i32ζ71+i32−ζ11−1−i32ζ111i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ11-1−i1i1−i32−ζ7−1+i32ζ71+i32−ζ11−1−i32ζ11
χ191-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32-11-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32-11-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ201−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ11-1i1−i1−i32ζ7−1+i32−ζ71+i32ζ11−1−i32−ζ111−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ11-1i1−i1−i32ζ7−1+i32−ζ71+i32ζ11−1−i32−ζ11
χ211111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32
χ221i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ7-1−i1i1+i32−ζ11−1−i32ζ111−i32−ζ7−1+i32ζ71i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ7-1−i1i1+i32−ζ11−1−i32ζ111−i32−ζ7−1+i32ζ7
χ231-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32-11-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32-11-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ241−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ7-1i1−i1+i32ζ11−1−i32−ζ111−i32ζ7−1+i32−ζ71−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ7-1i1−i1+i32ζ11−1−i32−ζ111−i32ζ7−1+i32−ζ7
χ25111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ261i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i
χ271-11-11-11-11-11-11-11-11-11-11-11-1-11-11-11-11-11-11-11-11-11-11-11-11
χ281−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i
χ291111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32
χ301i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ111i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ11-1−i1i1−i32−ζ7−1+i32ζ71+i32−ζ11−1−i32ζ11-1−i1i1−i32−ζ7−1+i32ζ71+i32−ζ11−1−i32ζ11
χ311-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32-11-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32-11-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ321−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ111−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ11-1i1−i1−i32ζ7−1+i32−ζ71+i32ζ11−1−i32−ζ11-1i1−i1−i32ζ7−1+i32−ζ71+i32ζ11−1−i32−ζ11
χ331111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32
χ341i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ71i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ7-1−i1i1+i32−ζ11−1−i32ζ111−i32−ζ7−1+i32ζ7-1−i1i1+i32−ζ11−1−i32ζ111−i32−ζ7−1+i32ζ7
χ351-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32-11-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32-11-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ361−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ71−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ7-1i1−i1+i32ζ11−1−i32−ζ111−i32ζ7−1+i32−ζ7-1i1−i1+i32ζ11−1−i32−ζ111−i32ζ7−1+i32−ζ7
χ37111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ381i-1−i1i-1−i1i-1−i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i1i-1−i1i-1−i1i-1−i
χ391-11-11-11-11-11-1-11-11-11-11-11-11-11-11-11-11-11-111-11-11-11-11-11-1
χ401−i-1i1−i-1i1−i-1i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i1−i-1i1−i-1i1−i-1i
χ411111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ421i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ11-1−i1i1−i32−ζ7−1+i32ζ71+i32−ζ11−1−i32ζ11-1−i1i1−i32−ζ7−1+i32ζ71+i32−ζ11−1−i32ζ111i-1−i−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ11
χ431-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32-11-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32-11-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ441−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ11-1i1−i1−i32ζ7−1+i32−ζ71+i32ζ11−1−i32−ζ11-1i1−i1−i32ζ7−1+i32−ζ71+i32ζ11−1−i32−ζ111−i-1i−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ11
χ451111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ461i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ7-1−i1i1+i32−ζ11−1−i32ζ111−i32−ζ7−1+i32ζ7-1−i1i1+i32−ζ11−1−i32ζ111−i32−ζ7−1+i32ζ71i-1−i−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ7
χ471-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32-11-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32-11-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ481−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ7-1i1−i1+i32ζ11−1−i32−ζ111−i32ζ7−1+i32−ζ7-1i1−i1+i32ζ11−1−i32−ζ111−i32ζ7−1+i32−ζ71−i-1i−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ7

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.