Finite Group Databasebeta

← Group #13166006

Character table — Group #13166006

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222333344446666666666666688888888888812121212161616161616161616161616181818181818242424242424242424242424363636363636363636363636108108108108
order124433661212121222443612122466666612121212121233366612121212121266121233366612121212121224661212666666121212121212888824242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11111-1-111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111-1-11111-1-111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-11111-1-1-1-111-1-111-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ611-1-11111-1-1-1-111-1-111-1-11-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ711-1-11111-1-1-1-111-1-111-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1111111i−ii−iii−i−iii−i−i−ii−ii
χ811-1-11111-1-1-1-111-1-111-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1111111−ii−ii−i−iii−i−iiii−ii−i
χ92222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1022222222222222222222-2-22222-2-222-2-222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111111110000000000000000
χ1122222-12-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1222-1-12-1-122-1-1-1-1-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-10000000000000000
χ1222222-12-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-122-12-1-12-1-1-122-1-1-1-1-1-1-12-1-12-1-1-122-1-122-1-1-1-1-1-122-1-1-1-122-1-10000000000000000
χ1322222-12-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-122-1-12-1-12-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1220000000000000000
χ1422222-12-1-1-1222222-1-1-1-1-2-222-1-111-1-111222-1-12-1-122-1-1-1-1-1-1-1-12-1-12-1-122-1-1-1-1-2-21111-2-21111-2-211110000000000000000
χ1522222-12-1-1-1222222-1-1-1-1-2-222-1-111-1-11122-12-1-12-1-1-122-1-1-1-1-1-1-12-1-12-1-1-122-1-1-2-2111111-2-21111-2-2110000000000000000
χ1622222-12-1-1-1222222-1-1-1-1-2-222-1-111-1-11122-1-12-1-12-1-1-1-122-1-1-1-1-1-12-1-12-1-1-1-122-2-211111111-2-21111-2-20000000000000000
χ172222-12-1222-1-12222-1-1-1-100-1-122002200-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-1-1-1-10000
χ182222-12-1222-1-12222-1-1-1-100-1-122002200-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2111111110000
χ1922-2-22222-2-2-2-222-2-222-2-22-2222222-2-2-2-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1-1-11111112-222-2-2-1-1-1-1-1-11111110000000000000000
χ2022-2-22222-2-2-2-222-2-222-2-2-222222-2-2-2-222-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1-1-1111111-22-2-222111111-1-1-1-1-1-10000000000000000
χ2122-2-22-12-111-2-222-2-2-1-1112-222-1-1-1-11111-2-22-1-12-1-1-2-21111-1-1112-1-12-1-1-2-211112-2-1-11122-1-1-1-1-2-211110000000000000000
χ2222-2-22-12-111-2-222-2-2-1-1112-222-1-1-1-11111-2-2-12-1-12-111-2-211-1-111-12-1-12-111-2-2112-2-1-111-1-122-1-111-2-2110000000000000000
χ2322-2-22-12-111-2-222-2-2-1-1112-222-1-1-1-11111-2-2-1-12-1-121111-2-2-1-111-1-12-1-121111-2-22-2-1-111-1-1-1-1221111-2-20000000000000000
χ2422-2-22-12-111-2-222-2-2-1-111-2222-1-11111-1-1-2-22-1-12-1-1-2-21111-1-1112-1-12-1-1-2-21111-2211-1-1-2-2111122-1-1-1-10000000000000000
χ2522-2-22-12-111-2-222-2-2-1-111-2222-1-11111-1-1-2-2-12-1-12-111-2-211-1-111-12-1-12-111-2-211-2211-1-111-2-211-1-122-1-10000000000000000
χ2622-2-22-12-111-2-222-2-2-1-111-2222-1-11111-1-1-2-2-1-12-1-121111-2-2-1-111-1-12-1-121111-2-2-2211-1-11111-2-2-1-1-1-1220000000000000000
χ2722-2-2-12-12-2-21122-2-2-1-11100-1-12200-2-20011222222-2-2-2-2-2-2-1-111-1-1-1-1-1-11111110000000000000000002i−2i2i−2i−i−iii−i−iii0000
χ2822-2-2-12-12-2-21122-2-2-1-11100-1-12200-2-20011222222-2-2-2-2-2-2-1-111-1-1-1-1-1-1111111000000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ292-22i−2i22-2-22i−2i2i−2i2-22i−2i2-22i−2i002-22-2002i−2i002i−2i222-2-2-22i−2i2i−2i2i−2i2-22i−2i222-2-2-22i−2i2i−2i2i−2i0000000000000000000000000000000000
χ302-22i−2i22-2-22i−2i2i−2i2-22i−2i2-22i−2i002-22-2002i−2i002i−2i-1-1-1111−ii−ii−ii2-22i−2i-1-1-1111−ii−ii−ii000000−i3i3−i3i3−i3i33−33−33−30000000000000000
χ312-22i−2i22-2-22i−2i2i−2i2-22i−2i2-22i−2i002-22-2002i−2i002i−2i-1-1-1111−ii−ii−ii2-22i−2i-1-1-1111−ii−ii−ii000000i3−i3i3−i3i3−i3−33−33−330000000000000000
χ322-22i−2i2-1-21−ii2i−2i2-22i−2i-11−ii002-2-11−i3i3−ii3−32i−2i2-1-1-2112i−2i−ii−ii-11−ii2-1-1-2112i−2i−ii−ii00−i3i33−300−i3i3i3−i3003−3−330000000000000000
χ332-22i−2i2-1-21−ii2i−2i2-22i−2i-11−ii002-2-11−i3i3−ii3−32i−2i-12-11-21−ii2i−2i−ii-11−ii-12-11-21−ii2i−2i−ii00−i3i33−3i3−i300−i3i3−33003−30000000000000000
χ342-22i−2i2-1-21−ii2i−2i2-22i−2i-11−ii002-2-11−i3i3−ii3−32i−2i-1-1211-2−ii−ii2i−2i-11−ii-1-1211-2−ii−ii2i−2i00−i3i33−3−i3i3i3−i3003−3−33000000000000000000
χ352-22i−2i2-1-21−ii2i−2i2-22i−2i-11−ii002-2-11i3−i3−ii−332i−2i2-1-1-2112i−2i−ii−ii-11−ii2-1-1-2112i−2i−ii−ii00i3−i3−3300i3−i3−i3i300−333−30000000000000000
χ362-22i−2i2-1-21−ii2i−2i2-22i−2i-11−ii002-2-11i3−i3−ii−332i−2i-12-11-21−ii2i−2i−ii-11−ii-12-11-21−ii2i−2i−ii00i3−i3−33−i3i300i3−i33−300−330000000000000000
χ372-22i−2i2-1-21−ii2i−2i2-22i−2i-11−ii002-2-11i3−i3−ii−332i−2i-1-1211-2−ii−ii2i−2i-11−ii-1-1211-2−ii−ii2i−2i00i3−i3−33i3−i3−i3i300−333−3000000000000000000
χ382-22i−2i-121-22i−2i−ii2-22i−2i-11−ii00-112-2002i−2i00−ii222-2-2-22i−2i2i−2i2i−2i-11−ii-1-1-1111−ii−ii−ii0000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ392-22i−2i-121-22i−2i−ii2-22i−2i-11−ii00-112-2002i−2i00−ii222-2-2-22i−2i2i−2i2i−2i-11−ii-1-1-1111−ii−ii−ii0000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ402-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i002-22-200−2i2i00−2i2i222-2-2-2−2i2i−2i2i−2i2i2-2−2i2i222-2-2-2−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ412-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i002-22-200−2i2i00−2i2i-1-1-1111i−ii−ii−i2-2−2i2i-1-1-1111i−ii−ii−i000000−i3i3−i3i3−i3i3−33−33−330000000000000000
χ422-2−2i2i22-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i002-22-200−2i2i00−2i2i-1-1-1111i−ii−ii−i2-2−2i2i-1-1-1111i−ii−ii−i000000i3−i3i3−i3i3−i33−33−33−30000000000000000
χ432-2−2i2i2-1-21i−i−2i2i2-2−2i2i-11i−i002-2-11−i3i3i−i−33−2i2i2-1-1-211−2i2ii−ii−i-11i−i2-1-1-211−2i2ii−ii−i00−i3i3−3300−i3i3i3−i300−333−30000000000000000
χ442-2−2i2i2-1-21i−i−2i2i2-2−2i2i-11i−i002-2-11−i3i3i−i−33−2i2i-12-11-21i−i−2i2ii−i-11i−i-12-11-21i−i−2i2ii−i00−i3i3−33i3−i300−i3i33−300−330000000000000000
χ452-2−2i2i2-1-21i−i−2i2i2-2−2i2i-11i−i002-2-11−i3i3i−i−33−2i2i-1-1211-2i−ii−i−2i2i-11i−i-1-1211-2i−ii−i−2i2i00−i3i3−33−i3i3i3−i300−333−3000000000000000000
χ462-2−2i2i2-1-21i−i−2i2i2-2−2i2i-11i−i002-2-11i3−i3i−i3−3−2i2i2-1-1-211−2i2ii−ii−i-11i−i2-1-1-211−2i2ii−ii−i00i3−i33−300i3−i3−i3i3003−3−330000000000000000
χ472-2−2i2i2-1-21i−i−2i2i2-2−2i2i-11i−i002-2-11i3−i3i−i3−3−2i2i-12-11-21i−i−2i2ii−i-11i−i-12-11-21i−i−2i2ii−i00i3−i33−3−i3i300i3−i3−33003−30000000000000000
χ482-2−2i2i2-1-21i−i−2i2i2-2−2i2i-11i−i002-2-11i3−i3i−i3−3−2i2i-1-1211-2i−ii−i−2i2i-11i−i-1-1211-2i−ii−i−2i2i00i3−i33−3i3−i3−i3i3003−3−33000000000000000000
χ492-2−2i2i-121-2−2i2ii−i2-2−2i2i-11i−i00-112-200−2i2i00i−i222-2-2-2−2i2i−2i2i−2i2i-11i−i-1-1-1111i−ii−ii−i0000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ502-2−2i2i-121-2−2i2ii−i2-2−2i2i-11i−i00-112-200−2i2i00i−i222-2-2-2−2i2i−2i2i−2i2i-11i−i-1-1-1111i−ii−ii−i0000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ51333333333333-1-1-1-1333333-1-1-1-133-1-133-1-1000000000000-1-1-1-1000000000000-1-1-1-1-1-100000000000011-1-11111-1-1-1-111-1-1
χ52333333333333-1-1-1-1333333-1-1-1-133-1-133-1-1000000000000-1-1-1-1000000000000-1-1-1-1-1-1000000000000-1-111-1-1-1-11111-1-111
χ53333333333333-1-1-1-13333-3-3-1-1-1-1-3-3-1-1-3-3-1-1000000000000-1-1-1-100000000000011111100000000000011-1-11111-1-1-1-1-1-111
χ54333333333333-1-1-1-13333-3-3-1-1-1-1-3-3-1-1-3-3-1-1000000000000-1-1-1-1000000000000111111000000000000-1-111-1-1-1-1111111-1-1
χ5533-3-33333-3-3-3-3-1-11133-3-33-3-1-1-1-13311-3-311000000000000-1-111000000000000-11-1-111000000000000i−i−iiii−i−i−i−iiii−i−ii
χ5633-3-33333-3-3-3-3-1-11133-3-33-3-1-1-1-13311-3-311000000000000-1-111000000000000-11-1-111000000000000−iii−i−i−iiiii−i−i−iii−i
χ5733-3-33333-3-3-3-3-1-11133-3-3-33-1-1-1-1-3-3113311000000000000-1-1110000000000001-111-1-1000000000000i−i−iiii−i−i−i−iii−iii−i
χ5833-3-33333-3-3-3-3-1-11133-3-3-33-1-1-1-1-3-3113311000000000000-1-1110000000000001-111-1-1000000000000−iii−i−i−iiiii−i−ii−i−ii
χ594444-24-2444-2-24444-2-2-2-200-2-244004400-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000000000
χ604444-2-2-2-2-2-2-2-24444111100-2-2-2-200-2-200-2-24-2-24-2-244-2-2-2-21111-211-211-2-211110000000000000000000000000000000000
χ614444-2-2-2-2-2-2-2-24444111100-2-2-2-200-2-200-2-2-24-2-24-2-2-244-2-211111-211-2111-2-2110000000000000000000000000000000000
χ624444-2-2-2-2-2-2-2-24444111100-2-2-2-200-2-200-2-2-2-24-2-24-2-2-2-244111111-211-21111-2-20000000000000000000000000000000000
χ6344-4-4-24-24-4-42244-4-4-2-22200-2-24400-4-40022-2-2-2-2-2-2222222-2-222111111-1-1-1-1-1-10000000000000000000000000000000000
χ6444-4-4-2-2-2-2222244-4-411-1-100-2-2-2-2002200224-2-24-2-2-4-4222211-1-1-211-21122-1-1-1-10000000000000000000000000000000000
χ6544-4-4-2-2-2-2222244-4-411-1-100-2-2-2-200220022-24-2-24-222-4-42211-1-11-211-21-1-122-1-10000000000000000000000000000000000
χ6644-4-4-2-2-2-2222244-4-411-1-100-2-2-2-200220022-2-24-2-242222-4-411-1-111-211-2-1-1-1-1220000000000000000000000000000000000
χ674-44i−4i-242-44i−4i−2i2i4-44i−4i-22−2i2i00-224-4004i−4i00−2i2i-2-2-2222−2i2i−2i2i−2i2i-22−2i2i111-1-1-1i−ii−ii−i0000000000000000000000000000000000
χ684-44i−4i-2-222−2i2i−2i2i4-44i−4i1-1i−i00-22-2200−2i2i00−2i2i4-2-2-4224i−4i−2i2i−2i2i1-1i−i-2112-1-1−2i2ii−ii−i0000000000000000000000000000000000
χ694-44i−4i-2-222−2i2i−2i2i4-44i−4i1-1i−i00-22-2200−2i2i00−2i2i-24-22-42−2i2i4i−4i−2i2i1-1i−i1-21-12-1i−i−2i2ii−i0000000000000000000000000000000000
χ704-44i−4i-2-222−2i2i−2i2i4-44i−4i1-1i−i00-22-2200−2i2i00−2i2i-2-2422-4−2i2i−2i2i4i−4i1-1i−i11-2-1-12i−ii−i−2i2i0000000000000000000000000000000000
χ714-4−4i4i-242-4−4i4i2i−2i4-4−4i4i-222i−2i00-224-400−4i4i002i−2i-2-2-22222i−2i2i−2i2i−2i-222i−2i111-1-1-1−ii−ii−ii0000000000000000000000000000000000
χ724-4−4i4i-2-2222i−2i2i−2i4-4−4i4i1-1−ii00-22-22002i−2i002i−2i4-2-2-422−4i4i2i−2i2i−2i1-1−ii-2112-1-12i−2i−ii−ii0000000000000000000000000000000000
χ734-4−4i4i-2-2222i−2i2i−2i4-4−4i4i1-1−ii00-22-22002i−2i002i−2i-24-22-422i−2i−4i4i2i−2i1-1−ii1-21-12-1−ii2i−2i−ii0000000000000000000000000000000000
χ744-4−4i4i-2-2222i−2i2i−2i4-4−4i4i1-1−ii00-22-22002i−2i002i−2i-2-2422-42i−2i2i−2i−4i4i1-1−ii11-2-1-12−ii−ii2i−2i0000000000000000000000000000000000
χ7566666-36-3-3-366-2-2-2-2-3-3-3-366-2-211-3-311-3-3-2-20000000000001111000000000000-2-211110000000000000000000000000000
χ7666666-36-3-3-366-2-2-2-2-3-3-3-3-6-6-2-211331133-2-2000000000000111100000000000022-1-1-1-10000000000000000000000000000
χ776666-36-3666-3-3-2-2-2-2-3-3-3-30011-2-200-2-20011000000000000111100000000000000000000000000000022-2-2-1-1-1-111110000
χ786666-36-3666-3-3-2-2-2-2-3-3-3-30011-2-200-2-200110000000000001111000000000000000000000000000000-2-2221111-1-1-1-10000
χ7966-6-66-36-333-6-6-2-222-3-3336-6-2-211-3-3-1-1332200000000000011-1-1000000000000-2211-1-10000000000000000000000000000
χ8066-6-66-36-333-6-6-2-222-3-333-66-2-21133-1-1-3-32200000000000011-1-10000000000002-2-1-1110000000000000000000000000000
χ8166-6-6-36-36-6-633-2-222-3-3330011-2-2002200-1-100000000000011-1-10000000000000000000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ8266-6-6-36-36-6-633-2-222-3-3330011-2-2002200-1-100000000000011-1-1000000000000000000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ836-66i−6i66-6-66i−6i6i−6i-22−2i2i6-66i−6i00-22-2200−2i2i00−2i2i000000000000-22−2i2i0000000000000000000000000000000000000000000000
χ846-66i−6i6-3-63−3i3i6i−6i-22−2i2i-33−3i3i00-221-1−3i33i3i−i33−33−2i2i0000000000001-1i−i00000000000000i3−i3−330000000000000000000000000000
χ856-66i−6i6-3-63−3i3i6i−6i-22−2i2i-33−3i3i00-221-13i3−3i3i−i−3333−2i2i0000000000001-1i−i00000000000000−i3i33−30000000000000000000000000000
χ866-66i−6i-363-66i−6i−3i3i-22−2i2i-33−3i3i001-1-2200−2i2i00i−i0000000000001-1i−i0000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ876-66i−6i-363-66i−6i−3i3i-22−2i2i-33−3i3i001-1-2200−2i2i00i−i0000000000001-1i−i0000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ886-6−6i6i66-6-6−6i6i−6i6i-222i−2i6-6−6i6i00-22-22002i−2i002i−2i000000000000-222i−2i0000000000000000000000000000000000000000000000
χ896-6−6i6i6-3-633i−3i−6i6i-222i−2i-333i−3i00-221-1−3i33i3−ii−33332i−2i0000000000001-1−ii00000000000000i3−i33−30000000000000000000000000000
χ906-6−6i6i6-3-633i−3i−6i6i-222i−2i-333i−3i00-221-13i3−3i3−ii33−332i−2i0000000000001-1−ii00000000000000−i3i3−330000000000000000000000000000
χ916-6−6i6i-363-6−6i6i3i−3i-222i−2i-333i−3i001-1-22002i−2i00−ii0000000000001-1−ii0000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ926-6−6i6i-363-6−6i6i3i−3i-222i−2i-333i−3i001-1-22002i−2i00−ii0000000000001-1−ii0000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ9312121212-6-6-6-6-6-6-6-6-4-4-4-4333300222200220022000000000000-1-1-1-10000000000000000000000000000000000000000000000
χ941212-12-12-6-6-6-66666-4-44433-3-300222200-2-200-2-2000000000000-1-1110000000000000000000000000000000000000000000000
χ9512-1212i−12i-6-666−6i6i−6i6i-44−4i4i3-33i−3i002-22-2002i−2i002i−2i000000000000-11−ii0000000000000000000000000000000000000000000000
χ9612-12−12i12i-6-6666i−6i6i−6i-444i−4i3-3−3i3i002-22-200−2i2i00−2i2i000000000000-11i−i0000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.