Finite Group Databasebeta

← Group #6839

Character table — Group #6839

Order 240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size145551455514555145551455514555145551455514555145551455514555
order152443156121231561212210244630612126306121221024463061212630612122102446306121263061212
χ1111111111111111111111111111111111111111111111111111111111111
χ2111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1
χ311-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i
χ411-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii
χ54-10004-10004-10004-10004-10004-10004-10004-10004-10004-10004-10004-1000
χ611111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ7111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32
χ811-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ1111-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ1111-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ1111-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ11
χ911-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ1111-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ1111-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ1111-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ11
χ104-1000−2+2i31−i32000−2−2i31+i320004-1000−2+2i31−i32000−2−2i31+i320004-1000−2+2i31−i32000−2−2i31+i320004-1000−2+2i31−i32000−2−2i31+i32000
χ1111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ12111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32
χ1311-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ711-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ711-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ711-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ7
χ1411-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ711-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ711-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ711-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ7
χ154-1000−2−2i31+i32000−2+2i31−i320004-1000−2−2i31+i32000−2+2i31−i320004-1000−2−2i31+i32000−2+2i31−i320004-1000−2−2i31+i32000−2+2i31−i32000
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ17111-1-1111-1-1111-1-1-1-1-111-1-1-111-1-1-111111-1-1111-1-1111-1-1-1-1-111-1-1-111-1-1-111
χ1811-1i−i11-1i−i11-1i−i-1-11−ii-1-11−ii-1-11−ii11-1i−i11-1i−i11-1i−i-1-11−ii-1-11−ii-1-11−ii
χ1911-1−ii11-1−ii11-1−ii-1-11i−i-1-11i−i-1-11i−i11-1−ii11-1−ii11-1−ii-1-11i−i-1-11i−i-1-11i−i
χ204-10004-10004-1000-41000-41000-410004-10004-10004-1000-41000-41000-41000
χ2111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i32
χ22111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32-1-1-1111−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32-1-1-1111−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32
χ2311-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ11-1-11−ii1−i321−i32−1+i32−ζ7ζ71+i321+i32−1−i32−ζ11ζ1111-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ11-1-11−ii1−i321−i32−1+i32−ζ7ζ71+i321+i32−1−i32−ζ11ζ11
χ2411-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ11-1-11i−i1−i321−i32−1+i32ζ7−ζ71+i321+i32−1−i32ζ11−ζ1111-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ11-1-11i−i1−i321−i32−1+i32ζ7−ζ71+i321+i32−1−i32ζ11−ζ11
χ254-1000−2+2i31−i32000−2−2i31+i32000-410002−2i3−1+i320002+2i3−1−i320004-1000−2+2i31−i32000−2−2i31+i32000-410002−2i3−1+i320002+2i3−1−i32000
χ2611111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−i321−i321−i321−i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−i321−i321−i321−i32
χ27111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1111+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1111+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32
χ2811-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ7-1-11−ii1+i321+i32−1−i32−ζ11ζ111−i321−i32−1+i32−ζ7ζ711-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ7-1-11−ii1+i321+i32−1−i32−ζ11ζ111−i321−i32−1+i32−ζ7ζ7
χ2911-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ7-1-11i−i1+i321+i32−1−i32ζ11−ζ111−i321−i32−1+i32ζ7−ζ711-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ7-1-11i−i1+i321+i32−1−i32ζ11−ζ111−i321−i32−1+i32ζ7−ζ7
χ304-1000−2−2i31+i32000−2+2i31−i32000-410002+2i3−1−i320002−2i3−1+i320004-1000−2−2i31+i32000−2+2i31−i32000-410002+2i3−1−i320002−2i3−1+i32000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ32111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1-1-1-111-1-1-111-1-1-111-1-1-111-1-1-111-1-1-111
χ3311-1i−i11-1i−i11-1i−i11-1i−i11-1i−i11-1i−i-1-11−ii-1-11−ii-1-11−ii-1-11−ii-1-11−ii-1-11−ii
χ3411-1−ii11-1−ii11-1−ii11-1−ii11-1−ii11-1−ii-1-11i−i-1-11i−i-1-11i−i-1-11i−i-1-11i−i-1-11i−i
χ354-10004-10004-10004-10004-10004-1000-41000-41000-41000-41000-41000-41000
χ3611111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i32
χ37111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32-1-1-1111−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32-1-1-1111−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32
χ3811-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ1111-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ11-1-11−ii1−i321−i32−1+i32−ζ7ζ71+i321+i32−1−i32−ζ11ζ11-1-11−ii1−i321−i32−1+i32−ζ7ζ71+i321+i32−1−i32−ζ11ζ11
χ3911-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ1111-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ11-1-11i−i1−i321−i32−1+i32ζ7−ζ71+i321+i32−1−i32ζ11−ζ11-1-11i−i1−i321−i32−1+i32ζ7−ζ71+i321+i32−1−i32ζ11−ζ11
χ404-1000−2+2i31−i32000−2−2i31+i320004-1000−2+2i31−i32000−2−2i31+i32000-410002−2i3−1+i320002+2i3−1−i32000-410002−2i3−1+i320002+2i3−1−i32000
χ4111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−i321−i321−i321−i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−i321−i321−i321−i32
χ42111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1111+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32-1-1-1111+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32
χ4311-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ711-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ7-1-11−ii1+i321+i32−1−i32−ζ11ζ111−i321−i32−1+i32−ζ7ζ7-1-11−ii1+i321+i32−1−i32−ζ11ζ111−i321−i32−1+i32−ζ7ζ7
χ4411-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ711-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ7-1-11i−i1+i321+i32−1−i32ζ11−ζ111−i321−i32−1+i32ζ7−ζ7-1-11i−i1+i321+i32−1−i32ζ11−ζ111−i321−i32−1+i32ζ7−ζ7
χ454-1000−2−2i31+i32000−2+2i31−i320004-1000−2−2i31+i32000−2+2i31−i32000-410002+2i3−1−i320002−2i3−1+i32000-410002+2i3−1−i320002−2i3−1+i32000
χ46111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111
χ47111-1-1111-1-1111-1-1-1-1-111-1-1-111-1-1-111-1-1-111-1-1-111-1-1-111111-1-1111-1-1111-1-1
χ4811-1i−i11-1i−i11-1i−i-1-11−ii-1-11−ii-1-11−ii-1-11−ii-1-11−ii-1-11−ii11-1i−i11-1i−i11-1i−i
χ4911-1−ii11-1−ii11-1−ii-1-11i−i-1-11i−i-1-11i−i-1-11i−i-1-11i−i-1-11i−i11-1−ii11-1−ii11-1−ii
χ504-10004-10004-1000-41000-41000-41000-41000-41000-410004-10004-10004-1000
χ5111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i32-1-1-1-1-11−i321−i321−i321−i321−i321+i321+i321+i321+i321+i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ52111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32-1-1-1111−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32-1-1-1111−i321−i321−i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32111-1-1−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32
χ5311-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ11-1-11−ii1−i321−i32−1+i32−ζ7ζ71+i321+i32−1−i32−ζ11ζ11-1-11−ii1−i321−i32−1+i32−ζ7ζ71+i321+i32−1−i32−ζ11ζ1111-1i−i−1+i32−1+i321−i32ζ7−ζ7−1−i32−1−i321+i32ζ11−ζ11
χ5411-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ11-1-11i−i1−i321−i32−1+i32ζ7−ζ71+i321+i32−1−i32ζ11−ζ11-1-11i−i1−i321−i32−1+i32ζ7−ζ71+i321+i32−1−i32ζ11−ζ1111-1−ii−1+i32−1+i321−i32−ζ7ζ7−1−i32−1−i321+i32−ζ11ζ11
χ554-1000−2+2i31−i32000−2−2i31+i32000-410002−2i3−1+i320002+2i3−1−i32000-410002−2i3−1+i320002+2i3−1−i320004-1000−2+2i31−i32000−2−2i31+i32000
χ5611111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−i321−i321−i321−i32-1-1-1-1-11+i321+i321+i321+i321+i321−i321−i321−i321−i321−i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ57111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1111+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32-1-1-1111+i321+i321+i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32111-1-1−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32
χ5811-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ7-1-11−ii1+i321+i32−1−i32−ζ11ζ111−i321−i32−1+i32−ζ7ζ7-1-11−ii1+i321+i32−1−i32−ζ11ζ111−i321−i32−1+i32−ζ7ζ711-1i−i−1−i32−1−i321+i32ζ11−ζ11−1+i32−1+i321−i32ζ7−ζ7
χ5911-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ7-1-11i−i1+i321+i32−1−i32ζ11−ζ111−i321−i32−1+i32ζ7−ζ7-1-11i−i1+i321+i32−1−i32ζ11−ζ111−i321−i32−1+i32ζ7−ζ711-1−ii−1−i32−1−i321+i32−ζ11ζ11−1+i32−1+i321−i32−ζ7ζ7
χ604-1000−2−2i31+i32000−2+2i31−i32000-410002+2i3−1−i320002−2i3−1+i32000-410002+2i3−1−i320002−2i3−1+i320004-1000−2−2i31+i32000−2+2i31−i32000

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