Finite Group Databasebeta

← Group #6331

Character table — Group #6331

Order 216.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size144999144999144999144999144999144999
order13324433361212333612122662446666121266661212
χ1111111111111111111111111111111111111
χ21111-1-11111-1-11111-1-11111-1-11111-1-11111-1-1
χ3111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i111-1i−i
χ4111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii111-1−ii
χ541-200041-200041-200041-200041-200041-2000
χ64-210004-210004-210004-210004-210004-21000
χ7111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ81111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ9111-1i−i−1+i32−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i32−1−i321+i32ζ11−ζ11111-1i−i−1+i32−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i32−1−i321+i32ζ11−ζ11
χ10111-1−ii−1+i32−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i32−1−i321+i32−ζ11ζ11111-1−ii−1+i32−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i32−1−i321+i32−ζ11ζ11
χ1141-2000−2+2i3−1+i321−i3000−2−2i3−1−i321+i300041-2000−2+2i3−1+i321−i3000−2−2i3−1−i321+i3000
χ124-21000−2+2i31−i3−1+i32000−2−2i31+i3−1−i320004-21000−2+2i31−i3−1+i32000−2−2i31+i3−1−i32000
χ13111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ141111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ15111-1i−i−1−i32−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i32−1+i321−i32ζ7−ζ7111-1i−i−1−i32−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i32−1+i321−i32ζ7−ζ7
χ16111-1−ii−1−i32−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i32−1+i321−i32−ζ7ζ7111-1−ii−1−i32−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i32−1+i321−i32−ζ7ζ7
χ1741-2000−2−2i3−1−i321+i3000−2+2i3−1+i321−i300041-2000−2−2i3−1−i321+i3000−2+2i3−1+i321−i3000
χ184-21000−2−2i31+i3−1−i32000−2+2i31−i3−1+i320004-21000−2−2i31+i3−1−i32000−2+2i31−i3−1+i32000
χ19111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ201111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111
χ21111-1i−i111-1i−i111-1i−i-1-1-11−ii-1-1-11−ii-1-1-11−ii
χ22111-1−ii111-1−ii111-1−ii-1-1-11i−i-1-1-11i−i-1-1-11i−i
χ2341-200041-200041-2000-4-12000-4-12000-4-12000
χ244-210004-210004-21000-42-1000-42-1000-42-1000
χ25111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32
χ261111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32-1-1-1-1111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32
χ27111-1i−i−1+i32−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i32−1−i321+i32ζ11−ζ11-1-1-11−ii1−i321−i321−i32−1+i32−ζ7ζ71+i321+i321+i32−1−i32−ζ11ζ11
χ28111-1−ii−1+i32−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i32−1−i321+i32−ζ11ζ11-1-1-11i−i1−i321−i321−i32−1+i32ζ7−ζ71+i321+i321+i32−1−i32ζ11−ζ11
χ2941-2000−2+2i3−1+i321−i3000−2−2i3−1−i321+i3000-4-120002−2i31−i32−1+i30002+2i31+i32−1−i3000
χ304-21000−2+2i31−i3−1+i32000−2−2i31+i3−1−i32000-42-10002−2i3−1+i31−i320002+2i3−1−i31+i32000
χ31111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32
χ321111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1-1111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32
χ33111-1i−i−1−i32−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i32−1+i321−i32ζ7−ζ7-1-1-11−ii1+i321+i321+i32−1−i32−ζ11ζ111−i321−i321−i32−1+i32−ζ7ζ7
χ34111-1−ii−1−i32−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i32−1+i321−i32−ζ7ζ7-1-1-11i−i1+i321+i321+i32−1−i32ζ11−ζ111−i321−i321−i32−1+i32ζ7−ζ7
χ3541-2000−2−2i3−1−i321+i3000−2+2i3−1+i321−i3000-4-120002+2i31+i32−1−i30002−2i31−i32−1+i3000
χ364-21000−2−2i31+i3−1−i32000−2+2i31−i3−1+i32000-42-10002+2i3−1−i31+i320002−2i3−1+i31−i32000

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