Finite Group Databasebeta

← Group #64257

Character table — Group #64257

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size113366668811336666881133666688113366668811336666881133666688
order1222444436366612121212363666121212123622224444666666121212126666661212121266
χ1111111111111111111111111111111111111111111111111111111111111
χ21111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ31-11-1i−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−i1-1
χ41-11-1−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−ii1-1
χ522220000-1-122220000-1-122220000-1-122220000-1-122220000-1-122220000-1-1
χ62-22-20000-112-22-20000-112-22-20000-112-22-20000-112-22-20000-112-22-20000-11
χ733-1-111-1-10033-1-111-1-10033-1-111-1-10033-1-111-1-10033-1-111-1-10033-1-111-1-100
χ833-1-1-1-1110033-1-1-1-1110033-1-1-1-1110033-1-1-1-1110033-1-1-1-1110033-1-1-1-11100
χ93-3-11i−i−ii003-3-11i−i−ii003-3-11i−i−ii003-3-11i−i−ii003-3-11i−i−ii003-3-11i−i−ii00
χ103-3-11−iii−i003-3-11−iii−i003-3-11−iii−i003-3-11−iii−i003-3-11−iii−i003-3-11−iii−i00
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
χ121111-1-1-1-111−1+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
χ131-11-1i−ii−i1-1−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i321-11-1i−ii−i1-1−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32
χ141-11-1−ii−ii1-1−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i321-11-1−ii−ii1-1−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32
χ1522220000-1-1−1+i3−1+i3−1+i3−1+i300001−i321−i32−1−i3−1−i3−1−i3−1−i300001+i321+i3222220000-1-1−1+i3−1+i3−1+i3−1+i300001−i321−i32−1−i3−1−i3−1−i3−1−i300001+i321+i32
χ162-22-20000-11−1+i31−i3−1+i31−i300001−i32−1+i32−1−i31+i3−1−i31+i300001+i32−1−i322-22-20000-11−1+i31−i3−1+i31−i300001−i32−1+i32−1−i31+i3−1−i31+i300001+i32−1−i32
χ1733-1-111-1-100−3+3i32−3+3i321−i321−i32−1+i32−1+i321−i321−i3200−3−3i32−3−3i321+i321+i32−1−i32−1−i321+i321+i320033-1-111-1-100−3+3i32−3+3i321−i321−i32−1+i32−1+i321−i321−i3200−3−3i32−3−3i321+i321+i32−1−i32−1−i321+i321+i3200
χ1833-1-1-1-11100−3+3i32−3+3i321−i321−i321−i321−i32−1+i32−1+i3200−3−3i32−3−3i321+i321+i321+i321+i32−1−i32−1−i320033-1-1-1-11100−3+3i32−3+3i321−i321−i321−i321−i32−1+i32−1+i3200−3−3i32−3−3i321+i321+i321+i321+i32−1−i32−1−i3200
χ193-3-11i−i−ii00−3+3i323−3i321−i32−1+i32ζ7−ζ7−ζ7ζ700−3−3i323+3i321+i32−1−i32ζ11−ζ11−ζ11ζ11003-3-11i−i−ii00−3+3i323−3i321−i32−1+i32ζ7−ζ7−ζ7ζ700−3−3i323+3i321+i32−1−i32ζ11−ζ11−ζ11ζ1100
χ203-3-11−iii−i00−3+3i323−3i321−i32−1+i32−ζ7ζ7ζ7−ζ700−3−3i323+3i321+i32−1−i32−ζ11ζ11ζ11−ζ11003-3-11−iii−i00−3+3i323−3i321−i32−1+i32−ζ7ζ7ζ7−ζ700−3−3i323+3i321+i32−1−i32−ζ11ζ11ζ11−ζ1100
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
χ221111-1-1-1-111−1−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
χ231-11-1i−ii−i1-1−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i321-11-1i−ii−i1-1−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32
χ241-11-1−ii−ii1-1−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i321-11-1−ii−ii1-1−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32
χ2522220000-1-1−1−i3−1−i3−1−i3−1−i300001+i321+i32−1+i3−1+i3−1+i3−1+i300001−i321−i3222220000-1-1−1−i3−1−i3−1−i3−1−i300001+i321+i32−1+i3−1+i3−1+i3−1+i300001−i321−i32
χ262-22-20000-11−1−i31+i3−1−i31+i300001+i32−1−i32−1+i31−i3−1+i31−i300001−i32−1+i322-22-20000-11−1−i31+i3−1−i31+i300001+i32−1−i32−1+i31−i3−1+i31−i300001−i32−1+i32
χ2733-1-111-1-100−3−3i32−3−3i321+i321+i32−1−i32−1−i321+i321+i3200−3+3i32−3+3i321−i321−i32−1+i32−1+i321−i321−i320033-1-111-1-100−3−3i32−3−3i321+i321+i32−1−i32−1−i321+i321+i3200−3+3i32−3+3i321−i321−i32−1+i32−1+i321−i321−i3200
χ2833-1-1-1-11100−3−3i32−3−3i321+i321+i321+i321+i32−1−i32−1−i3200−3+3i32−3+3i321−i321−i321−i321−i32−1+i32−1+i320033-1-1-1-11100−3−3i32−3−3i321+i321+i321+i321+i32−1−i32−1−i3200−3+3i32−3+3i321−i321−i321−i321−i32−1+i32−1+i3200
χ293-3-11i−i−ii00−3−3i323+3i321+i32−1−i32ζ11−ζ11−ζ11ζ1100−3+3i323−3i321−i32−1+i32ζ7−ζ7−ζ7ζ7003-3-11i−i−ii00−3−3i323+3i321+i32−1−i32ζ11−ζ11−ζ11ζ1100−3+3i323−3i321−i32−1+i32ζ7−ζ7−ζ7ζ700
χ303-3-11−iii−i00−3−3i323+3i321+i32−1−i32−ζ11ζ11ζ11−ζ1100−3+3i323−3i321−i32−1+i32−ζ7ζ7ζ7−ζ7003-3-11−iii−i00−3−3i323+3i321+i32−1−i32−ζ11ζ11ζ11−ζ1100−3+3i323−3i321−i32−1+i32−ζ7ζ7ζ7−ζ700
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
χ321111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ331-11-1i−ii−i1-11-11-1i−ii−i1-11-11-1i−ii−i1-1-11-11−ii−ii-11-11-11−ii−ii-11-11-11−ii−ii-11
χ341-11-1−ii−ii1-11-11-1−ii−ii1-11-11-1−ii−ii1-1-11-11i−ii−i-11-11-11i−ii−i-11-11-11i−ii−i-11
χ3522220000-1-122220000-1-122220000-1-1-2-2-2-2000011-2-2-2-2000011-2-2-2-2000011
χ362-22-20000-112-22-20000-112-22-20000-11-22-2200001-1-22-2200001-1-22-2200001-1
χ3733-1-111-1-10033-1-111-1-10033-1-111-1-100-3-311-1-11100-3-311-1-11100-3-311-1-11100
χ3833-1-1-1-1110033-1-1-1-1110033-1-1-1-11100-3-31111-1-100-3-31111-1-100-3-31111-1-100
χ393-3-11i−i−ii003-3-11i−i−ii003-3-11i−i−ii00-331-1−iii−i00-331-1−iii−i00-331-1−iii−i00
χ403-3-11−iii−i003-3-11−iii−i003-3-11−iii−i00-331-1i−i−ii00-331-1i−i−ii00-331-1i−i−ii00
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
χ421111-1-1-1-111−1+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
χ431-11-1i−ii−i1-1−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32-11-11−ii−ii-111−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ71−i32−1+i321+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ111+i32−1−i32
χ441-11-1−ii−ii1-1−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32-11-11i−ii−i-111−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ71−i32−1+i321+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ111+i32−1−i32
χ4522220000-1-1−1+i3−1+i3−1+i3−1+i300001−i321−i32−1−i3−1−i3−1−i3−1−i300001+i321+i32-2-2-2-20000111−i31−i31−i31−i30000−1+i32−1+i321+i31+i31+i31+i30000−1−i32−1−i32
χ462-22-20000-11−1+i31−i3−1+i31−i300001−i32−1+i32−1−i31+i3−1−i31+i300001+i32−1−i32-22-2200001-11−i3−1+i31−i3−1+i30000−1+i321−i321+i3−1−i31+i3−1−i30000−1−i321+i32
χ4733-1-111-1-100−3+3i32−3+3i321−i321−i32−1+i32−1+i321−i321−i3200−3−3i32−3−3i321+i321+i32−1−i32−1−i321+i321+i3200-3-311-1-111003−3i323−3i32−1+i32−1+i321−i321−i32−1+i32−1+i32003+3i323+3i32−1−i32−1−i321+i321+i32−1−i32−1−i3200
χ4833-1-1-1-11100−3+3i32−3+3i321−i321−i321−i321−i32−1+i32−1+i3200−3−3i32−3−3i321+i321+i321+i321+i32−1−i32−1−i3200-3-31111-1-1003−3i323−3i32−1+i32−1+i32−1+i32−1+i321−i321−i32003+3i323+3i32−1−i32−1−i32−1−i32−1−i321+i321+i3200
χ493-3-11i−i−ii00−3+3i323−3i321−i32−1+i32ζ7−ζ7−ζ7ζ700−3−3i323+3i321+i32−1−i32ζ11−ζ11−ζ11ζ1100-331-1−iii−i003−3i32−3+3i32−1+i321−i32−ζ7ζ7ζ7−ζ7003+3i32−3−3i32−1−i321+i32−ζ11ζ11ζ11−ζ1100
χ503-3-11−iii−i00−3+3i323−3i321−i32−1+i32−ζ7ζ7ζ7−ζ700−3−3i323+3i321+i32−1−i32−ζ11ζ11ζ11−ζ1100-331-1i−i−ii003−3i32−3+3i32−1+i321−i32ζ7−ζ7−ζ7ζ7003+3i32−3−3i32−1−i321+i32ζ11−ζ11−ζ11ζ1100
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
χ521111-1-1-1-111−1−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
χ531-11-1i−ii−i1-1−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1−i321+i32−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1+i321−i32-11-11−ii−ii-111+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ111+i32−1−i321−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ71−i32−1+i32
χ541-11-1−ii−ii1-1−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1−i321+i32−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1+i321−i32-11-11i−ii−i-111+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ111+i32−1−i321−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ71−i32−1+i32
χ5522220000-1-1−1−i3−1−i3−1−i3−1−i300001+i321+i32−1+i3−1+i3−1+i3−1+i300001−i321−i32-2-2-2-20000111+i31+i31+i31+i30000−1−i32−1−i321−i31−i31−i31−i30000−1+i32−1+i32
χ562-22-20000-11−1−i31+i3−1−i31+i300001+i32−1−i32−1+i31−i3−1+i31−i300001−i32−1+i32-22-2200001-11+i3−1−i31+i3−1−i30000−1−i321+i321−i3−1+i31−i3−1+i30000−1+i321−i32
χ5733-1-111-1-100−3−3i32−3−3i321+i321+i32−1−i32−1−i321+i321+i3200−3+3i32−3+3i321−i321−i32−1+i32−1+i321−i321−i3200-3-311-1-111003+3i323+3i32−1−i32−1−i321+i321+i32−1−i32−1−i32003−3i323−3i32−1+i32−1+i321−i321−i32−1+i32−1+i3200
χ5833-1-1-1-11100−3−3i32−3−3i321+i321+i321+i321+i32−1−i32−1−i3200−3+3i32−3+3i321−i321−i321−i321−i32−1+i32−1+i3200-3-31111-1-1003+3i323+3i32−1−i32−1−i32−1−i32−1−i321+i321+i32003−3i323−3i32−1+i32−1+i32−1+i32−1+i321−i321−i3200
χ593-3-11i−i−ii00−3−3i323+3i321+i32−1−i32ζ11−ζ11−ζ11ζ1100−3+3i323−3i321−i32−1+i32ζ7−ζ7−ζ7ζ700-331-1−iii−i003+3i32−3−3i32−1−i321+i32−ζ11ζ11ζ11−ζ11003−3i32−3+3i32−1+i321−i32−ζ7ζ7ζ7−ζ700
χ603-3-11−iii−i00−3−3i323+3i321+i32−1−i32−ζ11ζ11ζ11−ζ1100−3+3i323−3i321−i32−1+i32−ζ7ζ7ζ7−ζ700-331-1i−i−ii003+3i32−3−3i32−1−i321+i32ζ11−ζ11−ζ11ζ11003−3i32−3+3i32−1+i321−i32ζ7−ζ7−ζ7ζ700

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