Finite Group Databasebeta

← Group #218

Character table — Group #218

Order 48.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size111111111111111111111111111111111111111111111111
order142444442424444431261212121212612612121212123126121212121261261212121212
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
χ51111iiii-1-1-1-1−i−i−i−i1111iiii-1-1-1-1−i−i−i−i1111iiii-1-1-1-1−i−i−i−i
χ61i-1−ii-1−i1-1−i1i−i1i-11i-1−ii-1−i1-1−i1i−i1i-11i-1−ii-1−i1-1−i1i−i1i-1
χ71-11-1i−ii−i-11-11−ii−ii1-11-1i−ii−i-11-11−ii−ii1-11-1i−ii−i-11-11−ii−ii
χ81−i-1ii1−i-1-1i1−i−i-1i11−i-1ii1−i-1-1i1−i−i-1i11−i-1ii1−i-1-1i1−i−i-1i1
χ91111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101i-1−i-1−i1i1i-1−i-1−i1i1i-1−i-1−i1i1i-1−i-1−i1i1i-1−i-1−i1i1i-1−i-1−i1i
χ111-11-1-11-111-11-1-11-111-11-1-11-111-11-1-11-111-11-1-11-111-11-1-11-11
χ121−i-1i-1i1−i1−i-1i-1i1−i1−i-1i-1i1−i1−i-1i-1i1−i1−i-1i-1i1−i1−i-1i-1i1−i
χ131111−i−i−i−i-1-1-1-1iiii1111−i−i−i−i-1-1-1-1iiii1111−i−i−i−i-1-1-1-1iiii
χ141i-1−i−i1i-1-1−i1ii-1−i11i-1−i−i1i-1-1−i1ii-1−i11i-1−i−i1i-1-1−i1ii-1−i1
χ151-11-1−ii−ii-11-11i−ii−i1-11-1−ii−ii-11-11i−ii−i1-11-1−ii−ii-11-11i−ii−i
χ161−i-1i−i-1i1-1i1−ii1−i-11−i-1i−i-1i1-1i1−ii1−i-11−i-1i−i-1i1-1i1−ii1−i-1
χ171111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ181i-1−i1i-1−i1i-1−i1i-1−i−1+i32ζ71−i32−ζ7−1+i32ζ71−i32−ζ7−1+i32ζ71−i32−ζ7−1+i32ζ71−i32−ζ7−1−i32ζ111+i32−ζ11−1−i32ζ111+i32−ζ11−1−i32ζ111+i32−ζ11−1−i32ζ111+i32−ζ11
χ191-11-11-11-11-11-11-11-1−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32
χ201−i-1i1−i-1i1−i-1i1−i-1i−1+i32−ζ71−i32ζ7−1+i32−ζ71−i32ζ7−1+i32−ζ71−i32ζ7−1+i32−ζ71−i32ζ7−1−i32−ζ111+i32ζ11−1−i32−ζ111+i32ζ11−1−i32−ζ111+i32ζ11−1−i32−ζ111+i32ζ11
χ211111iiii-1-1-1-1−i−i−i−i−1+i32−1+i32−1+i32−1+i32ζ7ζ7ζ7ζ71−i321−i321−i321−i32−ζ7−ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32ζ11ζ11ζ11ζ111+i321+i321+i321+i32−ζ11−ζ11−ζ11−ζ11
χ221i-1−ii-1−i1-1−i1i−i1i-1−1+i32ζ71−i32−ζ7ζ71−i32−ζ7−1+i321−i32−ζ7−1+i32ζ7−ζ7−1+i32ζ71−i32−1−i32ζ111+i32−ζ11ζ111+i32−ζ11−1−i321+i32−ζ11−1−i32ζ11−ζ11−1−i32ζ111+i32
χ231-11-1i−ii−i-11-11−ii−ii−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ241−i-1ii1−i-1-1i1−i−i-1i1−1+i32−ζ71−i32ζ7ζ7−1+i32−ζ71−i321−i32ζ7−1+i32−ζ7−ζ71−i32ζ7−1+i32−1−i32−ζ111+i32ζ11ζ11−1−i32−ζ111+i321+i32ζ11−1−i32−ζ11−ζ111+i32ζ11−1−i32
χ251111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ261i-1−i-1−i1i1i-1−i-1−i1i−1+i32ζ71−i32−ζ71−i32−ζ7−1+i32ζ7−1+i32ζ71−i32−ζ71−i32−ζ7−1+i32ζ7−1−i32ζ111+i32−ζ111+i32−ζ11−1−i32ζ11−1−i32ζ111+i32−ζ111+i32−ζ11−1−i32ζ11
χ271-11-1-11-111-11-1-11-11−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ281−i-1i-1i1−i1−i-1i-1i1−i−1+i32−ζ71−i32ζ71−i32ζ7−1+i32−ζ7−1+i32−ζ71−i32ζ71−i32ζ7−1+i32−ζ7−1−i32−ζ111+i32ζ111+i32ζ11−1−i32−ζ11−1−i32−ζ111+i32ζ111+i32ζ11−1−i32−ζ11
χ291111−i−i−i−i-1-1-1-1iiii−1+i32−1+i32−1+i32−1+i32−ζ7−ζ7−ζ7−ζ71−i321−i321−i321−i32ζ7ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−ζ11−ζ11−ζ11−ζ111+i321+i321+i321+i32ζ11ζ11ζ11ζ11
χ301i-1−i−i1i-1-1−i1ii-1−i1−1+i32ζ71−i32−ζ7−ζ7−1+i32ζ71−i321−i32−ζ7−1+i32ζ7ζ71−i32−ζ7−1+i32−1−i32ζ111+i32−ζ11−ζ11−1−i32ζ111+i321+i32−ζ11−1−i32ζ11ζ111+i32−ζ11−1−i32
χ311-11-1−ii−ii-11-11i−ii−i−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11
χ321−i-1i−i-1i1-1i1−ii1−i-1−1+i32−ζ71−i32ζ7−ζ71−i32ζ7−1+i321−i32ζ7−1+i32−ζ7ζ7−1+i32−ζ71−i32−1−i32−ζ111+i32ζ11−ζ111+i32ζ11−1−i321+i32ζ11−1−i32−ζ11ζ11−1−i32−ζ111+i32
χ331111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ341i-1−i1i-1−i1i-1−i1i-1−i−1−i32ζ111+i32−ζ11−1−i32ζ111+i32−ζ11−1−i32ζ111+i32−ζ11−1−i32ζ111+i32−ζ11−1+i32ζ71−i32−ζ7−1+i32ζ71−i32−ζ7−1+i32ζ71−i32−ζ7−1+i32ζ71−i32−ζ7
χ351-11-11-11-11-11-11-11-1−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32
χ361−i-1i1−i-1i1−i-1i1−i-1i−1−i32−ζ111+i32ζ11−1−i32−ζ111+i32ζ11−1−i32−ζ111+i32ζ11−1−i32−ζ111+i32ζ11−1+i32−ζ71−i32ζ7−1+i32−ζ71−i32ζ7−1+i32−ζ71−i32ζ7−1+i32−ζ71−i32ζ7
χ371111iiii-1-1-1-1−i−i−i−i−1−i32−1−i32−1−i32−1−i32ζ11ζ11ζ11ζ111+i321+i321+i321+i32−ζ11−ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32ζ7ζ7ζ7ζ71−i321−i321−i321−i32−ζ7−ζ7−ζ7−ζ7
χ381i-1−ii-1−i1-1−i1i−i1i-1−1−i32ζ111+i32−ζ11ζ111+i32−ζ11−1−i321+i32−ζ11−1−i32ζ11−ζ11−1−i32ζ111+i32−1+i32ζ71−i32−ζ7ζ71−i32−ζ7−1+i321−i32−ζ7−1+i32ζ7−ζ7−1+i32ζ71−i32
χ391-11-1i−ii−i-11-11−ii−ii−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7
χ401−i-1ii1−i-1-1i1−i−i-1i1−1−i32−ζ111+i32ζ11ζ11−1−i32−ζ111+i321+i32ζ11−1−i32−ζ11−ζ111+i32ζ11−1−i32−1+i32−ζ71−i32ζ7ζ7−1+i32−ζ71−i321−i32ζ7−1+i32−ζ7−ζ71−i32ζ7−1+i32
χ411111-1-1-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ421i-1−i-1−i1i1i-1−i-1−i1i−1−i32ζ111+i32−ζ111+i32−ζ11−1−i32ζ11−1−i32ζ111+i32−ζ111+i32−ζ11−1−i32ζ11−1+i32ζ71−i32−ζ71−i32−ζ7−1+i32ζ7−1+i32ζ71−i32−ζ71−i32−ζ7−1+i32ζ7
χ431-11-1-11-111-11-1-11-11−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ441−i-1i-1i1−i1−i-1i-1i1−i−1−i32−ζ111+i32ζ111+i32ζ11−1−i32−ζ11−1−i32−ζ111+i32ζ111+i32ζ11−1−i32−ζ11−1+i32−ζ71−i32ζ71−i32ζ7−1+i32−ζ7−1+i32−ζ71−i32ζ71−i32ζ7−1+i32−ζ7
χ451111−i−i−i−i-1-1-1-1iiii−1−i32−1−i32−1−i32−1−i32−ζ11−ζ11−ζ11−ζ111+i321+i321+i321+i32ζ11ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−ζ7−ζ7−ζ7−ζ71−i321−i321−i321−i32ζ7ζ7ζ7ζ7
χ461i-1−i−i1i-1-1−i1ii-1−i1−1−i32ζ111+i32−ζ11−ζ11−1−i32ζ111+i321+i32−ζ11−1−i32ζ11ζ111+i32−ζ11−1−i32−1+i32ζ71−i32−ζ7−ζ7−1+i32ζ71−i321−i32−ζ7−1+i32ζ7ζ71−i32−ζ7−1+i32
χ471-11-1−ii−ii-11-11i−ii−i−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7
χ481−i-1i−i-1i1-1i1−ii1−i-1−1−i32−ζ111+i32ζ11−ζ111+i32ζ11−1−i321+i32ζ11−1−i32−ζ11ζ11−1−i32−ζ111+i32−1+i32−ζ71−i32ζ7−ζ71−i32ζ7−1+i321−i32ζ7−1+i32−ζ7ζ7−1+i32−ζ71−i32

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