Finite Group Databasebeta

← Group #956

Character table — Group #956

Order 96.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222211112222221111222222111122222211112222221111222222
order122244444436661212121212123666121212121212222244444466661212121212126666121212121212
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ31111-1-111-1-11111-1-111-1-11111-1-111-1-11111-1-111-1-11111-1-111-1-11111-1-111-1-1
χ41111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ51-11-11-1i−ii−i1-11-11-1i−ii−i1-11-11-1i−ii−i1-11-11-1i−ii−i1-11-11-1i−ii−i1-11-11-1i−ii−i
χ61-11-11-1−ii−ii1-11-11-1−ii−ii1-11-11-1−ii−ii1-11-11-1−ii−ii1-11-11-1−ii−ii1-11-11-1−ii−ii
χ71-11-1-11i−i−ii1-11-1-11i−i−ii1-11-1-11i−i−ii1-11-1-11i−i−ii1-11-1-11i−i−ii1-11-1-11i−i−ii
χ81-11-1-11−iii−i1-11-1-11−iii−i1-11-1-11−iii−i1-11-1-11−iii−i1-11-1-11−iii−i1-11-1-11−iii−i
χ922-2-200000022-2-200000022-2-200000022-2-200000022-2-200000022-2-2000000
χ102-2-220000002-2-220000002-2-220000002-2-220000002-2-220000002-2-22000000
χ111111111111−1+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−i321111111111−1+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
χ12111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ131111-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321111-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ141111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ151-11-11-1i−ii−i−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ111-11-11-1i−ii−i−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11
χ161-11-11-1−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ111-11-11-1−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11
χ171-11-1-11i−i−ii−1+i321−i32−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i321+i32−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ111-11-1-11i−i−ii−1+i321−i32−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i321+i32−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11
χ181-11-1-11−iii−i−1+i321−i32−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i321+i32−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ111-11-1-11−iii−i−1+i321−i32−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i321+i32−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11
χ1922-2-2000000−1+i3−1+i31−i31−i3000000−1−i3−1−i31+i31+i300000022-2-2000000−1+i3−1+i31−i31−i3000000−1−i3−1−i31+i31+i3000000
χ202-2-22000000−1+i31−i31−i3−1+i3000000−1−i31+i31+i3−1−i30000002-2-22000000−1+i31−i31−i3−1+i3000000−1−i31+i31+i3−1−i3000000
χ211111111111−1−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+i321111111111−1−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
χ22111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ231111-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321111-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ241111-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321111-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ251-11-11-1i−ii−i−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ71-11-11-1i−ii−i−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7
χ261-11-11-1−ii−ii−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ71-11-11-1−ii−ii−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7
χ271-11-1-11i−i−ii−1−i321+i32−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i321−i32−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ71-11-1-11i−i−ii−1−i321+i32−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i321−i32−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7
χ281-11-1-11−iii−i−1−i321+i32−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i321−i32−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ71-11-1-11−iii−i−1−i321+i32−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i321−i32−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7
χ2922-2-2000000−1−i3−1−i31+i31+i3000000−1+i3−1+i31−i31−i300000022-2-2000000−1−i3−1−i31+i31+i3000000−1+i3−1+i31−i31−i3000000
χ302-2-22000000−1−i31+i31+i3−1−i3000000−1+i31−i31−i3−1+i30000002-2-22000000−1−i31+i31+i3−1−i3000000−1+i31−i31−i3−1+i3000000
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
χ32111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ331111-1-111-1-11111-1-111-1-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-111
χ341111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ351-11-11-1i−ii−i1-11-11-1i−ii−i1-11-11-1i−ii−i-11-11-11−ii−ii-11-11-11−ii−ii-11-11-11−ii−ii
χ361-11-11-1−ii−ii1-11-11-1−ii−ii1-11-11-1−ii−ii-11-11-11i−ii−i-11-11-11i−ii−i-11-11-11i−ii−i
χ371-11-1-11i−i−ii1-11-1-11i−i−ii1-11-1-11i−i−ii-11-111-1−iii−i-11-111-1−iii−i-11-111-1−iii−i
χ381-11-1-11−iii−i1-11-1-11−iii−i1-11-1-11−iii−i-11-111-1i−i−ii-11-111-1i−i−ii-11-111-1i−i−ii
χ3922-2-200000022-2-200000022-2-2000000-2-222000000-2-222000000-2-222000000
χ402-2-220000002-2-220000002-2-22000000-222-2000000-222-2000000-222-2000000
χ411111111111−1+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−i32-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ42111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-1-1-1-1-1-111111−i321−i321−i321−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
χ431111-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32-1-1-1-111-1-1111−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ441111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32-1-1-1-11111-1-11−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ451-11-11-1i−ii−i−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11-11-11-11−ii−ii1−i32−1+i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ71+i32−1−i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11
χ461-11-11-1−ii−ii−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11-11-11-11i−ii−i1−i32−1+i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ71+i32−1−i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11
χ471-11-1-11i−i−ii−1+i321−i32−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−1−i321+i32−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11-11-111-1−iii−i1−i32−1+i321−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ71+i32−1−i321+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11
χ481-11-1-11−iii−i−1+i321−i32−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−1−i321+i32−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11-11-111-1i−i−ii1−i32−1+i321−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ71+i32−1−i321+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11
χ4922-2-2000000−1+i3−1+i31−i31−i3000000−1−i3−1−i31+i31+i3000000-2-2220000001−i31−i3−1+i3−1+i30000001+i31+i3−1−i3−1−i3000000
χ502-2-22000000−1+i31−i31−i3−1+i3000000−1−i31+i31+i3−1−i3000000-222-20000001−i3−1+i3−1+i31−i30000001+i3−1−i3−1−i31+i3000000
χ511111111111−1−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+i32-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32
χ52111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-1-1-1-1-1-111111+i321+i321+i321+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
χ531111-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32-1-1-1-111-1-1111+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ541111-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32-1-1-1-11111-1-11+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ551-11-11-1i−ii−i−1−i321+i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7-11-11-11−ii−ii1+i32−1−i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ111−i32−1+i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7
χ561-11-11-1−ii−ii−1−i321+i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7-11-11-11i−ii−i1+i32−1−i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ111−i32−1+i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7
χ571-11-1-11i−i−ii−1−i321+i32−1−i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−1+i321−i32−1+i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7-11-111-1−iii−i1+i32−1−i321+i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ111−i32−1+i321−i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7
χ581-11-1-11−iii−i−1−i321+i32−1−i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−1+i321−i32−1+i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7-11-111-1i−i−ii1+i32−1−i321+i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ111−i32−1+i321−i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7
χ5922-2-2000000−1−i3−1−i31+i31+i3000000−1+i3−1+i31−i31−i3000000-2-2220000001+i31+i3−1−i3−1−i30000001−i31−i3−1+i3−1+i3000000
χ602-2-22000000−1−i31+i31+i3−1−i3000000−1+i31−i31−i3−1+i3000000-222-20000001+i3−1−i3−1−i31+i30000001−i3−1+i3−1+i31−i3000000

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