Finite Group Databasebeta

← Group #13180279

Character table — Group #13180279

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222233333344666666666666889999991212121212121212121216161616181818181818181818181818242424242424242427273232363636363636363648484848545454547272
order12336622444436444466661212121236224444661212121212121212336622224444121212121212121212121212223666661212121212121212444466
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ31111111111-1-1111111111111-1-111-1-111-1-11111111111111111-1-111-1-111-1-11111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1
χ41111111111-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1
χ511111111-1-1111111111111-1-11111-1-1-1-11111111111111111-1-111-1-111-1-11111-1-11111-1-111-1-111-1-111-1-111-1-1-1-1-1-1
χ611111111-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ711111111-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ811111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ91-111-1-11-1i−ii−i1-1i−ii−i-1-111i−ii−i1-11-1i−ii−i1-1ii−i−iii−i−i11-1-11-11-11-11-1i−ii−ii−ii−ii−ii−i1-11-11-11-11-11-1i−ii−ii−ii−i1-1
χ101-111-1-11-1i−ii−i1-1−ii−ii-1-111i−ii−i1-11-1i−ii−i1-1−i−iii−i−iii11-1-1-11-11-11-11i−ii−i−iii−ii−i−ii1-11-1-11-11-11-11i−ii−i−ii−ii1-1
χ111-111-1-11-1i−i−ii1-1i−ii−i-1-111i−i−ii1-1-11i−i−ii1-1ii−i−iii−i−i11-1-11-1-111-1-11i−i−iii−ii−i−iii−i-111-11-1-111-1-11i−i−ii−ii−ii-11
χ121-111-1-11-1i−i−ii1-1−ii−ii-1-111i−i−ii1-1-11i−i−ii1-1−i−iii−i−iii11-1-1-111-1-111-1i−i−ii−iii−i−ii−ii-111-1-111-1-111-1i−i−iii−ii−i-11
χ131-111-1-11-1−iii−i1-1i−ii−i-1-111−iii−i1-1-11−iii−i1-1ii−i−iii−i−i11-1-1-111-1-111-1−iii−ii−i−iii−ii−i-111-1-111-1-111-1−iii−i−ii−ii-11
χ141-111-1-11-1−iii−i1-1−ii−ii-1-111−iii−i1-1-11−iii−i1-1−i−iii−i−iii11-1-11-1-111-1-11−iii−i−ii−iii−i−ii-111-11-1-111-1-11−iii−ii−ii−i-11
χ151-111-1-11-1−ii−ii1-1i−ii−i-1-111−ii−ii1-11-1−ii−ii1-1ii−i−iii−i−i11-1-1-11-11-11-11−ii−iii−i−ii−iii−i1-11-1-11-11-11-11−ii−iii−ii−i1-1
χ161-111-1-11-1−ii−ii1-1−ii−ii-1-111−ii−ii1-11-1−ii−ii1-1−i−iii−i−iii11-1-11-11-11-11-1−ii−ii−ii−ii−ii−ii1-11-11-11-11-11-1−ii−ii−ii−ii1-1
χ1722222222222222000022222222-1-12222222200000000-1-1-1-100000000222200-1-1-1-10022-1-100000000-1-1-1-10000-1-1
χ182222222222-2-2220000222222-2-2-1-1-2-222-2-22200000000-1-1-1-10000000022-2-200-1-11100-2-2-1-100000000-1-111000011
χ1922222222-2-2222200002222-2-222-1-1-2-2-2-2222200000000-1-1-1-100000000-2-2220011-1-100-2-2-1-10000000011-1-1000011
χ2022222222-2-2-2-22200002222-2-2-2-2-1-122-2-2-2-22200000000-1-1-1-100000000-2-2-2-20011110022-1-10000000011110000-1-1
χ21222-12-1220022-1-122222-12-100-1-122000022-1-12-12-12-12-12-12-10022002200-1-1-1-10022-1-100-1-100-1-100-1-100-1-1000000
χ22222-12-1220022-1-1-2-2-2-22-12-100-1-122000022-1-1-21-21-21-212-12-100-2-200-2-200-1-11100221100-1-10011001100-1-1000000
χ23222-12-12200-2-2-1-122222-12-10011220000-2-2-1-12-12-12-12-12-12-100-2-200-2-20011-1-100-2-2-1-100-1-1001100110011000000
χ24222-12-12200-2-2-1-1-2-2-2-22-12-10011220000-2-2-1-1-21-21-21-212-12-10022002200111100-2-21100-1-100-1-100-1-10011000000
χ2522-12-12222200-1-12222-12-12-1-10022002200-1-1-12-12-12-12-12-1222002200-1-100-1-12200-1-100-1-1-1-100-1-100-1-100000000
χ2622-12-12222200-1-1-2-2-2-2-12-12-1-10022002200-1-11-21-21-21-2-12-12-2-200-2-200-1-1001122001100-1-111001100-1-100000000
χ2722-12-1222-2-200-1-12222-12-1211002200-2-200-1-1-12-12-12-12-12-12-2-200-2-2001100-1-1-2-200-1-100-1-1110011001100000000
χ2822-12-1222-2-200-1-1-2-2-2-2-12-1211002200-2-200-1-11-21-21-21-2-12-1222002200110011-2-2001100-1-1-1-100-1-1001100000000
χ292-222-2-22-22i−2i2i−2i2-20000-2-2222i−2i2i−2i-112-22i−2i2i−2i2-200000000-1-111000000002i−2i2i−2i00−ii−ii002-2-1100000000−ii−ii0000-11
χ302-222-2-22-22i−2i−2i2i2-20000-2-2222i−2i−2i2i-11-222i−2i−2i2i2-200000000-1-111000000002i−2i−2i2i00−iii−i00-22-1100000000−iii−i00001-1
χ312-222-2-22-2−2i2i2i−2i2-20000-2-222−2i2i2i−2i-11-22−2i2i2i−2i2-200000000-1-11100000000−2i2i2i−2i00i−i−ii00-22-1100000000i−i−ii00001-1
χ322-222-2-22-2−2i2i−2i2i2-20000-2-222−2i2i−2i2i-112-2−2i2i−2i2i2-200000000-1-11100000000−2i2i−2i2i00i−ii−i002-2-1100000000i−ii−i0000-11
χ332-22-1-212-2002i−2i-112i−2i2i−2i-212-100−ii2-200002i−2i-112i−i−2ii2i−i−2ii2-1-21002-2002-200−ii−ii002i−2i−ii00-1100-1100-1100−ii000000
χ342-22-1-212-2002i−2i-11−2i2i−2i2i-212-100−ii2-200002i−2i-11−2ii2i−i−2ii2i−i2-1-2100-2200-2200−iii−i002i−2ii−i00-11001-1001-100−ii000000
χ352-22-1-212-200−2i2i-112i−2i2i−2i-212-100i−i2-20000−2i2i-112i−i−2ii2i−i−2ii2-1-2100-2200-2200i−i−ii00−2i2i−ii00-11001-1001-100i−i000000
χ362-22-1-212-200−2i2i-11−2i2i−2i2i-212-100i−i2-20000−2i2i-11−2ii2i−i−2ii2i−i2-1-21002-2002-200i−ii−i00−2i2ii−i00-1100-1100-1100i−i000000
χ372-2-121-22-22i−2i00-112i−2i2i−2i1-2-12−ii002-2002i−2i00-11−i2ii−2i−i2ii−2i-121-22-2002-200−ii00−ii2i−2i00−ii00-11-1100-1100−ii00000000
χ382-2-121-22-22i−2i00-11−2i2i−2i2i1-2-12−ii002-2002i−2i00-11i−2i−i2ii−2i−i2i-121-2-2200-2200−ii00i−i2i−2i00i−i00-111-1001-100−ii00000000
χ392-2-121-22-2−2i2i00-112i−2i2i−2i1-2-12i−i002-200−2i2i00-11−i2ii−2i−i2ii−2i-121-2-2200-2200i−i00−ii−2i2i00−ii00-111-1001-100i−i00000000
χ402-2-121-22-2−2i2i00-11−2i2i−2i2i1-2-12i−i002-200−2i2i00-11i−2i−i2ii−2i−i2i-121-22-2002-200i−i00i−i−2i2i00i−i00-11-1100-1100i−i00000000
χ41333333-1-133333311-1-1-1-1-1-133330033-1-1-1-1-1-11111-1-1-1-100001111-1-1-1-1-1-1-1-1110000-1-1-1-1001111-1-1-1-1000011-1-100
χ42333333-1-1333333-1-111-1-1-1-133330033-1-1-1-1-1-1-1-1-1-111110000-1-1-1-11111-1-1-1-1-1-1000011-1-100-1-1-1-111110000-1-11100
χ43333333-1-133-3-33311-1-1-1-1-1-133-3-300-3-3-1-111-1-11111-1-1-1-1000011-1-1-1-111-1-111110000-1-1110011-1-1-1-1110000-1-11100
χ44333333-1-133-3-333-1-111-1-1-1-133-3-300-3-3-1-111-1-1-1-1-1-111110000-1-11111-1-1-1-111-1-10000111100-1-11111-1-1000011-1-100
χ45333333-1-1-3-3333311-1-1-1-1-1-1-3-33300-3-311-1-1-1-11111-1-1-1-10000-1-11111-1-111-1-1110000-1-11100-1-11111-1-10000-1-11100
χ46333333-1-1-3-33333-1-111-1-1-1-1-3-33300-3-311-1-1-1-1-1-1-1-11111000011-1-1-1-11111-1-1-1-1000011110011-1-1-1-111000011-1-100
χ47333333-1-1-3-3-3-33311-1-1-1-1-1-1-3-3-3-300331111-1-11111-1-1-1-10000-1-1-1-111111111110000-1-1-1-100-1-1-1-11111000011-1-100
χ48333333-1-1-3-3-3-333-1-111-1-1-1-1-3-3-3-300331111-1-1-1-1-1-1111100001111-1-1-1-11111-1-1000011-1-1001111-1-1-1-10000-1-11100
χ493-333-3-3-113i−3i3i−3i3-3i−i−ii11-1-13i−3i3i−3i003-3−ii−ii-11ii−i−i−i−iii00001-11-1-11-11−ii−iii−i0000−ii-11001-11-1-11-110000i−i−ii00
χ503-333-3-3-113i−3i3i−3i3-3−iii−i11-1-13i−3i3i−3i003-3−ii−ii-11−i−iiiii−i−i0000-11-111-11-1−ii−ii−ii0000i−i-1100-11-111-11-10000−iii−i00
χ513-333-3-3-113i−3i−3i3i3-3i−i−ii11-1-13i−3i−3i3i00-33−iii−i-11ii−i−i−i−iii00001-1-11-111-1−iii−ii−i0000−ii1-1001-1-11-111-10000−iii−i00
χ523-333-3-3-113i−3i−3i3i3-3−iii−i11-1-13i−3i−3i3i00-33−iii−i-11−i−iiiii−i−i0000-111-11-1-11−iii−i−ii0000i−i1-100-111-11-1-110000i−i−ii00
χ533-333-3-3-11−3i3i3i−3i3-3i−i−ii11-1-1−3i3i3i−3i00-33i−i−ii-11ii−i−i−i−iii0000-111-11-1-11i−i−iii−i0000−ii1-100-111-11-1-110000−iii−i00
χ543-333-3-3-11−3i3i3i−3i3-3−iii−i11-1-1−3i3i3i−3i00-33i−i−ii-11−i−iiiii−i−i00001-1-11-111-1i−i−ii−ii0000i−i1-1001-1-11-111-10000i−i−ii00
χ553-333-3-3-11−3i3i−3i3i3-3i−i−ii11-1-1−3i3i−3i3i003-3i−ii−i-11ii−i−i−i−iii0000-11-111-11-1i−ii−ii−i0000−ii-1100-11-111-11-10000i−i−ii00
χ563-333-3-3-11−3i3i−3i3i3-3−iii−i11-1-1−3i3i−3i3i003-3i−ii−i-11−i−iiiii−i−i00001-11-1-11-11i−ii−i−ii0000i−i-11001-11-1-11-110000−iii−i00
χ57444-24-2440044-2-200004-24-200-2-2-2-2000044-2-200000000-21-210000000000-2-20000-2-2000011000000000011000000
χ58444-24-24400-4-4-2-200004-24-20022-2-20000-4-4-2-200000000-21-210000000000220000220000110000000000-1-1000000
χ5944-24-24444400-2-20000-24-24-2-200-2-2004400-2-2000000001-21-200000000-2-20000-2-200000011000000001100000000
χ6044-24-2444-4-400-2-20000-24-242200-2-200-4-400-2-2000000001-21-200000000220000220000001100000000-1-100000000
χ6144-2-2-2-2440000114444-2-2-2-200004400000011-2-2-2-2-2-2-2-2-2-2-2-2000000000000110000110011000000000000000000
χ6244-2-2-2-244000011-4-4-4-4-2-2-2-20000440000001122222222-2-2-2-2000000000000-1-10000-1-10011000000000000000000
χ634-44-2-424-4004i−4i-220000-424-200−2i2i-2200004i−4i-2200000000-212-10000000000−2i2i0000−2i2i00001-10000000000i−i000000
χ644-44-2-424-400−4i4i-220000-424-2002i−2i-220000−4i4i-2200000000-212-100000000002i−2i00002i−2i00001-10000000000−ii000000
χ654-4-242-44-44i−4i00-2200002-4-24−2i2i00-22004i−4i00-22000000001-2-1200000000−2i2i0000−2i2i0000001-100000000i−i00000000
χ664-4-242-44-4−4i4i00-2200002-4-242i−2i00-2200−4i4i00-22000000001-2-12000000002i−2i00002i−2i0000001-100000000−ii00000000
χ674-4-2-2224-400001-14i−4i4i−4i22-2-200004-40000001-1−2i−2i2i2i−2i−2i2i2i-2-222000000000000i−i0000i−i001-1000000000000000000
χ684-4-2-2224-400001-1−4i4i−4i4i22-2-200004-40000001-12i2i−2i−2i2i2i−2i−2i-2-222000000000000−ii0000−ii001-1000000000000000000
χ69666-36-3-2-20066-3-322-2-2-21-2100-3-3000000-2-2112-12-1-21-210000002200-2-20011-1-1000011000000-1-100110000000000
χ70666-36-3-2-20066-3-3-2-222-21-2100-3-3000000-2-211-21-212-12-1000000-2-200220011110000-1-10000001100-1-10000000000
χ71666-36-3-2-200-6-6-3-322-2-2-21-21003300000022112-12-1-21-21000000-2-2002200-1-1-1-10000110000001100-1-10000000000
χ72666-36-3-2-200-6-6-3-3-2-222-21-2100330000002211-21-212-12-10000002200-2-200-1-1110000-1-1000000-1-100110000000000
χ7366-36-36-2-26600-3-322-2-21-21-2-3-3000000-2-20011-12-121-21-200002200-2-2001100-1-10000110000-1-10011000000000000
χ7466-36-36-2-26600-3-3-2-2221-21-2-3-3000000-2-200111-21-2-12-120000-2-20022001100110000-1-100001100-1-1000000000000
χ7566-36-36-2-2-6-600-3-322-2-21-21-233000000220011-12-121-21-20000-2-2002200-1-100-1-100001100001100-1-1000000000000
χ7666-36-36-2-2-6-600-3-3-2-2221-21-2330000002200111-21-2-12-1200002200-2-200-1-100110000-1-10000-1-10011000000000000
χ776-66-3-63-22006i−6i-332i−2i−2i2i2-1-2100−3i3i000000−2i2i1-12i−i−2ii−2ii2i−i0000002-200-2200i−i−ii0000i−i000000-11001-10000000000
χ786-66-3-63-22006i−6i-33−2i2i2i−2i2-1-2100−3i3i000000−2i2i1-1−2ii2i−i2i−i−2ii000000-22002-200i−ii−i0000−ii0000001-100-110000000000
χ796-66-3-63-2200−6i6i-332i−2i−2i2i2-1-21003i−3i0000002i−2i1-12i−i−2ii−2ii2i−i000000-22002-200−ii−ii0000i−i0000001-100-110000000000
χ806-66-3-63-2200−6i6i-33−2i2i2i−2i2-1-21003i−3i0000002i−2i1-1−2ii2i−i2i−i−2ii0000002-200-2200−iii−i0000−ii000000-11001-10000000000
χ816-6-363-6-226i−6i00-332i−2i−2i2i-121-2−3i3i000000−2i2i001-1−i2ii−2ii−2i−i2i00002-200-2200i−i00−ii0000i−i0000-11001-1000000000000
χ826-6-363-6-226i−6i00-33−2i2i2i−2i-121-2−3i3i000000−2i2i001-1i−2i−i2i−i2ii−2i0000-22002-200i−i00i−i0000−ii00001-100-11000000000000
χ836-6-363-6-22−6i6i00-332i−2i−2i2i-121-23i−3i0000002i−2i001-1−i2ii−2ii−2i−i2i0000-22002-200−ii00−ii0000i−i00001-100-11000000000000
χ846-6-363-6-22−6i6i00-33−2i2i2i−2i-121-23i−3i0000002i−2i001-1i−2i−i2i−i2ii−2i00002-200-2200−ii00i−i0000−ii0000-11001-1000000000000
χ8588-4-4-4-4880000220000-4-4-4-40000-4-4000000220000000022220000000000000000000000-1-1000000000000000000
χ868-8-4-4448-800002-2000044-4-40000-440000002-20000000022-2-20000000000000000000000-11000000000000000000
χ871212-6-6-6-6-4-400003344-4-42222000000000000-1-1-2-2-2-222220000000000000000110000-1-10000000000000000000000
χ881212-6-6-6-6-4-4000033-4-4442222000000000000-1-12222-2-2-2-20000000000000000-1-10000110000000000000000000000
χ8912-12-6-666-4400003-34i−4i−4i4i-2-222000000000000-11−2i−2i2i2i2i2i−2i−2i0000000000000000i−i0000−ii0000000000000000000000
χ9012-12-6-666-4400003-3−4i4i4i−4i-2-222000000000000-112i2i−2i−2i−2i−2i2i2i0000000000000000−ii0000i−i0000000000000000000000

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