Finite Group Databasebeta

← Group #13170708

Character table — Group #13170708

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122222222224444444444446666666699991212121212121212181822224444444444888888888888121212121212121218181818242424242424242436363333666666666612121212121212121212121218181818181818182727272736363636363636365454
order122233446666663666121212121212121244444444222212121212121212124436663312126666663666121212121212121212121212121212126666121212121212121212122222664466666666661212121212121212444444442222121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ6111111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111
χ7111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ8111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ91-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i11-1-11-11-1i−ii−ii−i1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i11-1-11-11-1i−ii−ii−i1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i11-1-11-11-1i−ii−ii−i
χ101-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-1-11i−i−ii-1-1111-1-11i−i−ii−ii1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-1-11i−i−ii-1-1111-1-11i−i−ii−ii1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-1-11i−i−ii-1-1111-1-11i−i−ii−ii
χ111-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-111-1−iii−i-1-111-111-1−iii−i−ii1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-111-1−iii−i-1-111-111-1−iii−i−ii1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-111-1−iii−i-1-111-111-1−iii−i−ii
χ121-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-11-11−ii−ii11-1-1-11-11−ii−iii−i1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-11-11−ii−ii11-1-1-11-11−ii−iii−i1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-11-11−ii−ii11-1-1-11-11−ii−iii−i
χ131-11-111−ii-1-111-1-111-1-1−i−iii−i−iii1-11-1−ii−ii11-1-11-11-1−ii−ii−ii1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii1-11-1−ii−ii11-1-11-11-1−ii−ii−ii1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii1-11-1−ii−ii11-1-11-11-1−ii−ii−ii
χ141-11-111−ii-1-111-1-111-1-1−i−iii−i−iii1-1-11−iii−i-1-1111-1-11−iii−ii−i1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii1-1-11−iii−i-1-1111-1-11−iii−ii−i1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii1-1-11−iii−i-1-1111-1-11−iii−ii−i
χ151-11-111−ii-1-111-1-111-1-1−i−iii−i−iii-111-1i−i−ii-1-111-111-1i−i−iii−i1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii-111-1i−i−ii-1-111-111-1i−i−iii−i1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii-111-1i−i−ii-1-111-111-1i−i−iii−i
χ161-11-111−ii-1-111-1-111-1-1−i−iii−i−iii-11-11i−ii−i11-1-1-11-11i−ii−i−ii1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii-11-11i−ii−i11-1-1-11-11i−ii−i−ii1-11-111−ii-1-111-1-111-1-1−i−iii−i−iii-11-11i−ii−i11-1-1-11-11i−ii−i−ii
χ1722222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100220022000000-1-100-1-10022222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100220022000000-1-100-1-10022222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100220022000000-1-100-1-100
χ1822222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100-2-200-2-20000001100110022222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100-2-200-2-20000001100110022222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100-2-200-2-200000011001100
χ1922222-1-2-22-12-12-1-1-1-1-1-21-211111002200-2-2000000-1-100110022222-1-2-22-12-12-1-1-1-1-1-21-211111002200-2-2000000-1-100110022222-1-2-22-12-12-1-1-1-1-1-21-211111002200-2-2000000-1-1001100
χ2022222-1-2-22-12-12-1-1-1-1-1-21-21111100-2-200220000001100-1-10022222-1-2-22-12-12-1-1-1-1-1-21-21111100-2-200220000001100-1-10022222-1-2-22-12-12-1-1-1-1-1-21-21111100-2-200220000001100-1-100
χ212222-1222-12-12-12-1-1-1-1-12-12-1-1-1-1220022000000-1-100-1-100002222-1222-12-12-12-1-1-1-1-12-12-1-1-1-1220022000000-1-100-1-100002222-1222-12-12-12-1-1-1-1-12-12-1-1-1-1220022000000-1-100-1-10000
χ222222-1222-12-12-12-1-1-1-1-12-12-1-1-1-1-2-200-2-200000011001100002222-1222-12-12-12-1-1-1-1-12-12-1-1-1-1-2-200-2-200000011001100002222-1222-12-12-12-1-1-1-1-12-12-1-1-1-1-2-200-2-20000001100110000
χ232222-12-2-2-12-12-12-1-1-1-11-21-211112200-2-2000000-1-1001100002222-12-2-2-12-12-12-1-1-1-11-21-211112200-2-2000000-1-1001100002222-12-2-2-12-12-12-1-1-1-11-21-211112200-2-2000000-1-100110000
χ242222-12-2-2-12-12-12-1-1-1-11-21-21111-2-200220000001100-1-100002222-12-2-2-12-12-12-1-1-1-11-21-21111-2-200220000001100-1-100002222-12-2-2-12-12-12-1-1-1-11-21-21111-2-200220000001100-1-10000
χ2522-2-2220022-2-2-2-22-22-200000000000000002-22-2000000000022-2-2220022-2-2-2-22-22-200000000000000002-22-2000000000022-2-2220022-2-2-2-22-22-200000000000000002-22-20000000000
χ2622-2-2220022-2-2-2-22-22-20000000000000000-22-22000000000022-2-2220022-2-2-2-22-22-20000000000000000-22-22000000000022-2-2220022-2-2-2-22-22-20000000000000000-22-220000000000
χ272-22-22-12i−2i-212-1-21-1-1112i−i−2ii−i−iii002-2002i−2i000000-1100−ii002-22-22-12i−2i-212-1-21-1-1112i−i−2ii−i−iii002-2002i−2i000000-1100−ii002-22-22-12i−2i-212-1-21-1-1112i−i−2ii−i−iii002-2002i−2i000000-1100−ii00
χ282-22-22-12i−2i-212-1-21-1-1112i−i−2ii−i−iii00-2200−2i2i0000001-100i−i002-22-22-12i−2i-212-1-21-1-1112i−i−2ii−i−iii00-2200−2i2i0000001-100i−i002-22-22-12i−2i-212-1-21-1-1112i−i−2ii−i−iii00-2200−2i2i0000001-100i−i00
χ292-22-22-1−2i2i-212-1-21-1-111−2ii2i−iii−i−i002-200−2i2i000000-1100i−i002-22-22-1−2i2i-212-1-21-1-111−2ii2i−iii−i−i002-200−2i2i000000-1100i−i002-22-22-1−2i2i-212-1-21-1-111−2ii2i−iii−i−i002-200−2i2i000000-1100i−i00
χ302-22-22-1−2i2i-212-1-21-1-111−2ii2i−iii−i−i00-22002i−2i0000001-100−ii002-22-22-1−2i2i-212-1-21-1-111−2ii2i−iii−i−i00-22002i−2i0000001-100−ii002-22-22-1−2i2i-212-1-21-1-111−2ii2i−iii−i−i00-22002i−2i0000001-100−ii00
χ312-22-2-122i−2i1-2-121-2-1-111−i2ii−2i−i−iii2-2002i−2i000000-1100−ii00002-22-2-122i−2i1-2-121-2-1-111−i2ii−2i−i−iii2-2002i−2i000000-1100−ii00002-22-2-122i−2i1-2-121-2-1-111−i2ii−2i−i−iii2-2002i−2i000000-1100−ii0000
χ322-22-2-122i−2i1-2-121-2-1-111−i2ii−2i−i−iii-2200−2i2i0000001-100i−i00002-22-2-122i−2i1-2-121-2-1-111−i2ii−2i−i−iii-2200−2i2i0000001-100i−i00002-22-2-122i−2i1-2-121-2-1-111−i2ii−2i−i−iii-2200−2i2i0000001-100i−i0000
χ332-22-2-12−2i2i1-2-121-2-1-111i−2i−i2iii−i−i2-200−2i2i000000-1100i−i00002-22-2-12−2i2i1-2-121-2-1-111i−2i−i2iii−i−i2-200−2i2i000000-1100i−i00002-22-2-12−2i2i1-2-121-2-1-111i−2i−i2iii−i−i2-200−2i2i000000-1100i−i0000
χ342-22-2-12−2i2i1-2-121-2-1-111i−2i−i2iii−i−i-22002i−2i0000001-100−ii00002-22-2-12−2i2i1-2-121-2-1-111i−2i−i2iii−i−i-22002i−2i0000001-100−ii00002-22-2-12−2i2i1-2-121-2-1-111i−2i−i2iii−i−i-22002i−2i0000001-100−ii0000
χ352-2-222200-2-2-2-2222-2-2200000000000000002-2-2200000000002-2-222200-2-2-2-2222-2-2200000000000000002-2-2200000000002-2-222200-2-2-2-2222-2-2200000000000000002-2-220000000000
χ362-2-222200-2-2-2-2222-2-220000000000000000-222-200000000002-2-222200-2-2-2-2222-2-220000000000000000-222-200000000002-2-222200-2-2-2-2222-2-220000000000000000-222-20000000000
χ374444-2-244-2-2-2-2-2-21111-2-2-2-2111100000000000000000000004444-2-244-2-2-2-2-2-21111-2-2-2-2111100000000000000000000004444-2-244-2-2-2-2-2-21111-2-2-2-211110000000000000000000000
χ384444-2-2-4-4-2-2-2-2-2-211112222-1-1-1-100000000000000000000004444-2-2-4-4-2-2-2-2-2-211112222-1-1-1-100000000000000000000004444-2-2-4-4-2-2-2-2-2-211112222-1-1-1-10000000000000000000000
χ3944-4-44-2004-2-42-42-22-2200000000000000000000000000000044-4-44-2004-2-42-42-22-2200000000000000000000000000000044-4-44-2004-2-42-42-22-22000000000000000000000000000000
χ4044-4-4-2400-242-42-4-22-2200000000000000000000000000000044-4-4-2400-242-42-4-22-2200000000000000000000000000000044-4-4-2400-242-42-4-22-22000000000000000000000000000000
χ4144-4-4-2-200-2-222221-11-100003i−3i3i−3i000000000000000000000044-4-4-2-200-2-222221-11-100003i−3i3i−3i000000000000000000000044-4-4-2-200-2-222221-11-100003i−3i3i−3i0000000000000000000000
χ4244-4-4-2-200-2-222221-11-10000−3i3i−3i3i000000000000000000000044-4-4-2-200-2-222221-11-10000−3i3i−3i3i000000000000000000000044-4-4-2-200-2-222221-11-10000−3i3i−3i3i0000000000000000000000
χ434-44-4-2-24i−4i22-2-22211-1-1−2i−2i2i2iii−i−i00000000000000000000004-44-4-2-24i−4i22-2-22211-1-1−2i−2i2i2iii−i−i00000000000000000000004-44-4-2-24i−4i22-2-22211-1-1−2i−2i2i2iii−i−i0000000000000000000000
χ444-44-4-2-2−4i4i22-2-22211-1-12i2i−2i−2i−i−iii00000000000000000000004-44-4-2-2−4i4i22-2-22211-1-12i2i−2i−2i−i−iii00000000000000000000004-44-4-2-2−4i4i22-2-22211-1-12i2i−2i−2i−i−iii0000000000000000000000
χ454-4-444-200-42-424-2-222-20000000000000000000000000000004-4-444-200-42-424-2-222-20000000000000000000000000000004-4-444-200-42-424-2-222-2000000000000000000000000000000
χ464-4-44-24002-42-4-24-222-20000000000000000000000000000004-4-44-24002-42-4-24-222-20000000000000000000000000000004-4-44-24002-42-4-24-222-2000000000000000000000000000000
χ474-4-44-2-2002222-2-21-1-1100003-3-3300000000000000000000004-4-44-2-2002222-2-21-1-1100003-3-3300000000000000000000004-4-44-2-2002222-2-21-1-1100003-3-330000000000000000000000
χ484-4-44-2-2002222-2-21-1-110000-333-300000000000000000000004-4-44-2-2002222-2-21-1-110000-333-300000000000000000000004-4-44-2-2002222-2-21-1-110000-333-30000000000000000000000
χ49111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ501111111111111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-11111
χ5111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-111-1-111
χ5211111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ53111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ54111111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-11111-1-1-1-1
χ55111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-111-1-1
χ56111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ571-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i11-1-11-11-1i−ii−ii−i1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i11-1-11-11-1i−ii−ii−i-11-11-1-1−ii11-1-111-1-111−i−iii−i−iii-11-11−ii−ii-1-111-11-11−ii−ii−ii
χ581-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-1-11i−i−ii-1-1111-1-11i−i−ii−ii1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i1-1-11i−i−ii-1-1111-1-11i−i−ii−ii-11-11-1-1−ii11-1-111-1-111−i−iii−i−iii-111-1−iii−i11-1-1-111-1−iii−ii−i
χ591-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-111-1−iii−i-1-111-111-1−iii−i−ii1-11-111i−i-1-111-1-111-1-1ii−i−iii−i−i-111-1−iii−i-1-111-111-1−iii−i−ii-11-11-1-1−ii11-1-111-1-111−i−iii−i−iii1-1-11i−i−ii11-1-11-1-11i−i−iii−i
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χ1338888-4-488-4-4-4-4-4-42222-4-4-4-422220000000000000000000000-4-4-4-422-4-4222222-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000000000000000000000
χ1348888-4-4-8-8-4-4-4-4-4-422224444-2-2-2-20000000000000000000000-4-4-4-42244222222-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000000000000000000
χ13588-8-88-4008-4-84-84-44-44000000000000000000000000000000-4-444-4200-424-24-22-22-2000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13688-8-8-4800-484-84-8-44-44000000000000000000000000000000-4-4442-4002-4-24-242-22-2000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13788-8-8-4-400-4-444442-22-200006i−6i6i−6i0000000000000000000000-4-444220022-2-2-2-2-11-110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000000000000
χ13888-8-8-4-400-4-444442-22-20000−6i6i−6i6i0000000000000000000000-4-444220022-2-2-2-2-11-1100003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000000000000
χ1398-88-8-4-48i−8i44-4-44422-2-2−4i−4i4i4i2i2i−2i−2i0000000000000000000000-44-4422−4i4i-2-222-2-2-1-1112i2i−2i−2i−i−iii0000000000000000000000000000000000000000000000000000000000000000000000
χ1408-88-8-4-4−8i8i44-4-44422-2-24i4i−4i−4i−2i−2i2i2i0000000000000000000000-44-44224i−4i-2-222-2-2-1-111−2i−2i2i2iii−i−i0000000000000000000000000000000000000000000000000000000000000000000000
χ1418-8-888-400-84-848-4-444-4000000000000000000000000000000-444-4-42004-24-2-422-2-22000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-8-88-48004-84-8-48-444-4000000000000000000000000000000-444-42-400-24-242-42-2-22000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1438-8-88-4-4004444-4-42-2-2200006-6-660000000000000000000000-444-42200-2-2-2-222-111-10000-333-30000000000000000000000000000000000000000000000000000000000000000000000
χ1448-8-88-4-4004444-4-42-2-220000-666-60000000000000000000000-444-42200-2-2-2-222-111-100003-3-330000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).