Finite Group Databasebeta

← Group #6282

Character table — Group #6282

Order 216.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size112233224466336699112233224466336699112233224466336699
order12364436361212226644363612123636121266661212363612123636121266661212
χ1111111111111111111111111111111111111111111111111111111
χ21111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-11111-1-1
χ31-11-1i−i1-11-1i−i1-11-1i−i1-11-1i−i1-11-1i−i1-11-1i−i1-11-1i−i1-11-1i−i1-11-1i−i
χ41-11-1−ii1-11-1−ii1-11-1−ii1-11-1−ii1-11-1−ii1-11-1−ii1-11-1−ii1-11-1−ii1-11-1−ii
χ522-1-10022-1-10022-1-10022-1-10022-1-10022-1-10022-1-10022-1-10022-1-100
χ62-2-11002-2-11002-2-11002-2-11002-2-11002-2-11002-2-11002-2-11002-2-1100
χ7111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ81111-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ91-11-1i−i1-11-1i−i-11-11−ii1-11-1i−i1-11-1i−i-11-11−ii1-11-1i−i1-11-1i−i-11-11−ii
χ101-11-1−ii1-11-1−ii-11-11i−i1-11-1−ii1-11-1−ii-11-11i−i1-11-1−ii1-11-1−ii-11-11i−i
χ1122-1-10022-1-100-2-2110022-1-10022-1-100-2-2110022-1-10022-1-100-2-21100
χ122-2-11002-2-1100-221-1002-2-11002-2-1100-221-1002-2-11002-2-1100-221-100
χ13222222-1-1-1-1-1-1000000222222-1-1-1-1-1-1000000222222-1-1-1-1-1-1000000
χ142222-2-2-1-1-1-1110000002222-2-2-1-1-1-1110000002222-2-2-1-1-1-111000000
χ152-22-22i−2i-11-11−ii0000002-22-22i−2i-11-11−ii0000002-22-22i−2i-11-11−ii000000
χ162-22-2−2i2i-11-11i−i0000002-22-2−2i2i-11-11i−i0000002-22-2−2i2i-11-11i−i000000
χ1744-2-200-2-2110000000044-2-200-2-2110000000044-2-200-2-21100000000
χ184-4-2200-221-1000000004-4-2200-221-1000000004-4-2200-221-100000000
χ19111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32
χ201111-1-11111-1-11111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ211-11-1i−i1-11-1i−i1-11-1i−i−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11
χ221-11-1−ii1-11-1−ii1-11-1−ii−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11
χ2322-1-10022-1-10022-1-100−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i3200−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i3200
χ242-2-11002-2-11002-2-1100−1+i31−i31−i32−1+i3200−1+i31−i31−i32−1+i3200−1+i31−i31−i32−1+i3200−1−i31+i31+i32−1−i3200−1−i31+i31+i32−1−i3200−1−i31+i31+i32−1−i3200
χ25111111111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ261111-1-11111-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ271-11-1i−i1-11-1i−i-11-11−ii−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11
χ281-11-1−ii1-11-1−ii-11-11i−i−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11
χ2922-1-10022-1-100-2-21100−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i32001−i31−i3−1+i32−1+i3200−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i32001+i31+i3−1−i32−1−i3200
χ302-2-11002-2-1100-221-100−1+i31−i31−i32−1+i3200−1+i31−i31−i32−1+i32001−i3−1+i3−1+i321−i3200−1−i31+i31+i32−1−i3200−1−i31+i31+i32−1−i32001+i3−1−i3−1−i321+i3200
χ31222222-1-1-1-1-1-1000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32000000
χ322222-2-2-1-1-1-111000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i321−i321−i321−i32−1+i32−1+i32000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i321+i321+i321+i32−1−i32−1−i32000000
χ332-22-22i−2i-11-11−ii000000−1+i31−i3−1+i31−i32ζ7−2ζ71−i32−1+i321−i32−1+i32−ζ7ζ7000000−1−i31+i3−1−i31+i32ζ11−2ζ111+i32−1−i321+i32−1−i32−ζ11ζ11000000
χ342-22-2−2i2i-11-11i−i000000−1+i31−i3−1+i31−i3−2ζ72ζ71−i32−1+i321−i32−1+i32ζ7−ζ7000000−1−i31+i3−1−i31+i3−2ζ112ζ111+i32−1−i321+i32−1−i32ζ11−ζ11000000
χ3544-2-200-2-21100000000−2+2i3−2+2i31−i31−i3001−i31−i3−1+i32−1+i3200000000−2−2i3−2−2i31+i31+i3001+i31+i3−1−i32−1−i3200000000
χ364-4-2200-221-100000000−2+2i32−2i31−i3−1+i3001−i3−1+i3−1+i321−i3200000000−2−2i32+2i31+i3−1−i3001+i3−1−i3−1−i321+i3200000000
χ37111111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32
χ381111-1-11111-1-11111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ391-11-1i−i1-11-1i−i1-11-1i−i−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7
χ401-11-1−ii1-11-1−ii1-11-1−ii−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7
χ4122-1-10022-1-10022-1-100−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i3200−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i3200
χ422-2-11002-2-11002-2-1100−1−i31+i31+i32−1−i3200−1−i31+i31+i32−1−i3200−1−i31+i31+i32−1−i3200−1+i31−i31−i32−1+i3200−1+i31−i31−i32−1+i3200−1+i31−i31−i32−1+i3200
χ43111111111111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32
χ441111-1-11111-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ451-11-1i−i1-11-1i−i-11-11−ii−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ111+i32−1−i321+i32−1−i32−ζ11ζ11−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ71−i32−1+i321−i32−1+i32−ζ7ζ7
χ461-11-1−ii1-11-1−ii-11-11i−i−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ111+i32−1−i321+i32−1−i32ζ11−ζ11−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ71−i32−1+i321−i32−1+i32ζ7−ζ7
χ4722-1-10022-1-100-2-21100−1−i3−1−i31+i321+i3200−1−i3−1−i31+i321+i32001+i31+i3−1−i32−1−i3200−1+i3−1+i31−i321−i3200−1+i3−1+i31−i321−i32001−i31−i3−1+i32−1+i3200
χ482-2-11002-2-1100-221-100−1−i31+i31+i32−1−i3200−1−i31+i31+i32−1−i32001+i3−1−i3−1−i321+i3200−1+i31−i31−i32−1+i3200−1+i31−i31−i32−1+i32001−i3−1+i3−1+i321−i3200
χ49222222-1-1-1-1-1-1000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32000000
χ502222-2-2-1-1-1-111000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i321+i321+i321+i32−1−i32−1−i32000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i321−i321−i321−i32−1+i32−1+i32000000
χ512-22-22i−2i-11-11−ii000000−1−i31+i3−1−i31+i32ζ11−2ζ111+i32−1−i321+i32−1−i32−ζ11ζ11000000−1+i31−i3−1+i31−i32ζ7−2ζ71−i32−1+i321−i32−1+i32−ζ7ζ7000000
χ522-22-2−2i2i-11-11i−i000000−1−i31+i3−1−i31+i3−2ζ112ζ111+i32−1−i321+i32−1−i32ζ11−ζ11000000−1+i31−i3−1+i31−i3−2ζ72ζ71−i32−1+i321−i32−1+i32ζ7−ζ7000000
χ5344-2-200-2-21100000000−2−2i3−2−2i31+i31+i3001+i31+i3−1−i32−1−i3200000000−2+2i3−2+2i31−i31−i3001−i31−i3−1+i32−1+i3200000000
χ544-4-2200-221-100000000−2−2i32+2i31+i3−1−i3001+i3−1−i3−1−i321+i3200000000−2+2i32−2i31−i3−1+i3001−i3−1+i3−1+i321−i3200000000

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