Finite Group Databasebeta

← Group #5440

Character table — Group #5440

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size11112222224444444466666666888888888888
order12224444443366666622444444121212121212121212121212
χ111111111111111111111111111111111111111
χ21111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ31111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ4111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-1
χ5111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ6111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ71111-1-111-1-111111111-1-111-1-111-1-1-1-1-1-111-1-111
χ81111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ91111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ101111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ111111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ121111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ131-11-1i−ii−i1-111-1-111-1-11-11-1i−ii−i1-11-1i−ii−ii−ii−i
χ141-11-1i−ii−i1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-11-1i−ii−i−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ151-11-1i−ii−i1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-11-1i−ii−i−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ161-11-1i−i−ii-1111-1-111-1-1-111-1i−i−ii-11-11i−i−iii−i−ii
χ171-11-1i−i−ii-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32-111-1i−i−ii1+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ181-11-1i−i−ii-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32-111-1i−i−ii1−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ191-11-1−iii−i-1111-1-111-1-1-111-1−iii−i-11-11−iii−i−iii−i
χ201-11-1−iii−i-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32-111-1−iii−i1+i32−1−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ211-11-1−iii−i-11−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32-111-1−iii−i1−i32−1+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ221-11-1−ii−ii1-111-1-111-1-11-11-1−ii−ii1-11-1−ii−ii−ii−ii
χ231-11-1−ii−ii1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-11-1−ii−ii−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ241-11-1−ii−ii1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-11-1−ii−ii−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ25333333333300000000-1-1-1-1-1-1-1-1000000000000
χ26333333-3-3-3-30000000011-1-1-1-111000000000000
χ273333-3-333-3-30000000011-1-111-1-1000000000000
χ283333-3-3-3-33300000000-1-1-1-11111000000000000
χ293-33-33i−3i3i−3i3-300000000-11-11−ii−ii000000000000
χ303-33-33i−3i−3i3i-33000000001-1-11−iii−i000000000000
χ313-33-3−3i3i3i−3i-33000000001-1-11i−i−ii000000000000
χ323-33-3−3i3i−3i3i3-300000000-11-11i−ii−i000000000000
χ3344-4-4000000-2-22222-2-200000000000000000000
χ3444-4-40000001+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000000000000000000
χ3544-4-40000001−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000000000000000000
χ364-4-44000000-2-2-2-2222200000000000000000000
χ374-4-440000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i300000000000000000000
χ384-4-440000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i300000000000000000000

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