Finite Group Databasebeta

← Group #11721121

Character table — Group #11721121

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111122222222226666666699991212121212121212121212121818181818181818181818181818181818183636363636363636
order122234466612121212336666664444366612121212121212122244444444121212121212121266121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111
χ711111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ811111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ91-11-11i−i-11-1ii−i−i11-11-11-1-111-1-111-1-1i−ii−iii−i−i1-1i−ii−ii−i1-111-1-1ii−i−i1-1i−i1-1i−i
χ101-11-11i−i-11-1ii−i−i11-11-11-1-111-1-111-1-1i−ii−iii−i−i-11−iii−i−ii-1111-1-1ii−i−i-11−ii-11−ii
χ111-11-11i−i-11-1ii−i−i11-11-11-1-1-1-11111-1-1i−ii−iii−i−i1-1−ii−iii−i-11-1-111−i−iii1-1i−i-11−ii
χ121-11-11i−i-11-1ii−i−i11-11-11-1-1-1-11111-1-1i−ii−iii−i−i-11i−i−ii−ii1-1-1-111−i−iii-11−ii1-1i−i
χ131-11-11−ii-11-1−i−iii11-11-11-1-111-1-111-1-1−ii−ii−i−iii1-1−ii−ii−ii1-111-1-1−i−iii1-1−ii1-1−ii
χ141-11-11−ii-11-1−i−iii11-11-11-1-111-1-111-1-1−ii−ii−i−iii-11i−i−iii−i-1111-1-1−i−iii-11i−i-11i−i
χ151-11-11−ii-11-1−i−iii11-11-11-1-1-1-11111-1-1−ii−ii−i−iii1-1i−ii−i−ii-11-1-111ii−i−i1-1−ii-11i−i
χ161-11-11−ii-11-1−i−iii11-11-11-1-1-1-11111-1-1−ii−ii−i−iii-11−iii−ii−i1-1-1-111ii−i−i-11i−i1-1−ii
χ17222222222222222-12-1-12-120000-1-1-1-1-1-122-1-1-1-1220000220000000000-1-1-1-10000
χ18222222222222222-12-1-12-120000-1-1-1-1-1-122-1-1-1-1-2-20000-2-2000000000011110000
χ1922222222222222-12-122-12-10000-1-1-1-122-1-1-1-1-1-10022000022000000000000-1-1-1-1
χ2022222222222222-12-122-12-10000-1-1-1-122-1-1-1-1-1-100-2-20000-2-20000000000001111
χ2122222-2-2222-2-2-2-22-12-1-12-120000-1-1-1-111-2-21111220000-2-20000000000-1-1110000
χ2222222-2-2222-2-2-2-22-12-1-12-120000-1-1-1-111-2-21111-2-2000022000000000011-1-10000
χ2322222-2-2222-2-2-2-2-12-122-12-10000-1-1-1-1-2-211111100220000-2-200000000000011-1-1
χ2422222-2-2222-2-2-2-2-12-122-12-10000-1-1-1-1-2-211111100-2-2000022000000000000-1-111
χ2522-2-22002-2-2000022-2-22-2-222i−2i2i−2i2-2-220000000000000000002i−2i2i−2i000000000000
χ2622-2-22002-2-2000022-2-22-2-22−2i2i−2i2i2-2-22000000000000000000−2i2i−2i2i000000000000
χ272-22-222i−2i-22-22i2i−2i−2i2-1-2-1121-20000-1-111−ii2i−2i−i−iii2-200002i−2i0000000000-11−ii0000
χ282-22-222i−2i-22-22i2i−2i−2i2-1-2-1121-20000-1-111−ii2i−2i−i−iii-220000−2i2i00000000001-1i−i0000
χ292-22-222i−2i-22-22i2i−2i−2i-1212-2-1-210000-1-1112i−2i−ii−i−iii002i−2i00002-2000000000000-11−ii
χ302-22-222i−2i-22-22i2i−2i−2i-1212-2-1-210000-1-1112i−2i−ii−i−iii00−2i2i0000-220000000000001-1i−i
χ312-22-22−2i2i-22-2−2i−2i2i2i2-1-2-1121-20000-1-111i−i−2i2iii−i−i2-20000−2i2i0000000000-11i−i0000
χ322-22-22−2i2i-22-2−2i−2i2i2i2-1-2-1121-20000-1-111i−i−2i2iii−i−i-2200002i−2i00000000001-1−ii0000
χ332-22-22−2i2i-22-2−2i−2i2i2i-1212-2-1-210000-1-111−2i2ii−iii−i−i002i−2i0000-220000000000001-1−ii
χ342-22-22−2i2i-22-2−2i−2i2i2i-1212-2-1-210000-1-111−2i2ii−iii−i−i00−2i2i00002-2000000000000-11i−i
χ352-2-22200-2-220000222-2-2-22-22i−2i−2i2i2-22-20000000000000000002i−2i−2i2i000000000000
χ362-2-22200-2-220000222-2-2-22-2−2i2i2i−2i2-22-2000000000000000000−2i2i2i−2i000000000000
χ3744444444444444-2-2-2-2-2-2-2-200001111-2-2-2-2111100000000000000000000000000
χ3844444-4-4444-4-4-4-4-2-2-2-2-2-2-2-2000011112222-1-1-1-100000000000000000000000000
χ3944-4-44004-4-400004-2-42-2-4240000-222-20000000000000000000000000000000000
χ4044-4-44004-4-40000-242-442-4-20000-222-20000000000000000000000000000000000
χ4144-4-44004-4-40000-2-222-222-200001-1-1100003-33-300000000000000000000000000
χ4244-4-44004-4-40000-2-222-222-200001-1-110000-33-3300000000000000000000000000
χ434-44-444i−4i-44-44i4i−4i−4i-2-22-22-222000011-1-1−2i2i−2i2iii−i−i00000000000000000000000000
χ444-44-44−4i4i-44-4−4i−4i4i4i-2-22-22-222000011-1-12i−2i2i−2i−i−iii00000000000000000000000000
χ454-4-44400-4-4400004-2422-4-2-40000-22-220000000000000000000000000000000000
χ464-4-44400-4-440000-24-2-4-42420000-22-220000000000000000000000000000000000
χ474-4-44400-4-440000-2-2-2222-2200001-11-100003i−3i−3i3i00000000000000000000000000
χ484-4-44400-4-440000-2-2-2222-2200001-11-10000−3i3i3i−3i00000000000000000000000000
χ496666-366-3-3-3-3-3-3-30000000022220000000000000000220000-1-1-1-1-1-1-1-100000000
χ506666-366-3-3-3-3-3-3-300000000-2-2-2-20000000000000000-2-200001111111100000000
χ516666-3-6-6-3-3-333330000000022220000000000000000-2-20000-1-1-1-1111100000000
χ526666-3-6-6-3-3-3333300000000-2-2-2-200000000000000002200001111-1-1-1-100000000
χ5366-6-6-300-333−3i33i3−3i33i3000000002i−2i2i−2i0000000000000000000000−ii−ii3−33−300000000
χ5466-6-6-300-333−3i33i3−3i33i300000000−2i2i−2i2i0000000000000000000000i−ii−i−33−3300000000
χ5566-6-6-300-3333i3−3i33i3−3i3000000002i−2i2i−2i0000000000000000000000−ii−ii−33−3300000000
χ5666-6-6-300-3333i3−3i33i3−3i300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−300000000
χ576-66-6-36i−6i3-33−3i−3i3i3i0000000022-2-200000000000000002i−2i0000-1-111−i−iii00000000
χ586-66-6-36i−6i3-33−3i−3i3i3i00000000-2-2220000000000000000−2i2i000011-1-1ii−i−i00000000
χ596-66-6-3−6i6i3-333i3i−3i−3i0000000022-2-20000000000000000−2i2i0000-1-111ii−i−i00000000
χ606-66-6-3−6i6i3-333i3i−3i−3i00000000-2-22200000000000000002i−2i000011-1-1−i−iii00000000
χ616-6-66-30033-333−33−3333000000002i−2i−2i2i0000000000000000000000−iii−ii3−i3−i3i300000000
χ626-6-66-30033-333−33−333300000000−2i2i2i−2i0000000000000000000000i−i−ii−i3i3i3−i300000000
χ636-6-66-30033-3−333333−33000000002i−2i−2i2i0000000000000000000000−iii−i−i3i3i3−i300000000
χ646-6-66-30033-3−333333−3300000000−2i2i2i−2i0000000000000000000000i−i−iii3−i3−i3i300000000

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