Finite Group Databasebeta

← Group #11721124

Character table — Group #11721124

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111122222222226666666699991212121212121212121212121818181818181818181818181818181818183636363636363636
order12223446661212121233666666444436661212121212121212222244444466661212121266121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ711111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111-1-1
χ811111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-111
χ911-1-11i−i1-1-1ii−i−i11-11-11-1-1ii−i−i11-1-1i−ii−iii−i−i1-11-1i−i1-1i−i11-1-1ii−i−i1-1i−i1-1i−i
χ1011-1-11i−i1-1-1ii−i−i11-11-11-1-1ii−i−i11-1-1i−ii−iii−i−i1-1-11−ii-11−ii11-1-1ii−i−i-11−ii-11−ii
χ1111-1-11i−i1-1-1ii−i−i11-11-11-1-1−i−iii11-1-1i−ii−iii−i−i-111-1i−i-11−ii-1-111−i−iii1-1i−i-11−ii
χ1211-1-11i−i1-1-1ii−i−i11-11-11-1-1−i−iii11-1-1i−ii−iii−i−i-11-11−ii1-1i−i-1-111−i−iii-11−ii1-1i−i
χ1311-1-11−ii1-1-1−i−iii11-11-11-1-1ii−i−i11-1-1−ii−ii−i−iii-111-1−ii-11i−i-1-111ii−i−i1-1−ii-11i−i
χ1411-1-11−ii1-1-1−i−iii11-11-11-1-1ii−i−i11-1-1−ii−ii−i−iii-11-11i−i1-1−ii-1-111ii−i−i-11i−i1-1−ii
χ1511-1-11−ii1-1-1−i−iii11-11-11-1-1−i−iii11-1-1−ii−ii−i−iii1-11-1−ii1-1−ii11-1-1−i−iii1-1−ii1-1−ii
χ1611-1-11−ii1-1-1−i−iii11-11-11-1-1−i−iii11-1-1−ii−ii−i−iii1-1-11i−i-11i−i11-1-1−i−iii-11i−i-11i−i
χ17222222222222222-12-1-12-120000-1-1-1-1-1-122-1-1-1-1002222000000000000-1-1-1-10000
χ18222222222222222-12-1-12-120000-1-1-1-1-1-122-1-1-1-100-2-2-2-200000000000011110000
χ1922222222222222-12-122-12-10000-1-1-1-122-1-1-1-1-1-10000002222000000000000-1-1-1-1
χ2022222222222222-12-122-12-10000-1-1-1-122-1-1-1-1-1-1000000-2-2-2-20000000000001111
χ2122222-2-2222-2-2-2-22-12-1-12-120000-1-1-1-111-2-211110022-2-2000000000000-1-1110000
χ2222222-2-2222-2-2-2-22-12-1-12-120000-1-1-1-111-2-2111100-2-22200000000000011-1-10000
χ2322222-2-2222-2-2-2-2-12-122-12-10000-1-1-1-1-2-211111100000022-2-2000000000000-1-111
χ2422222-2-2222-2-2-2-2-12-122-12-10000-1-1-1-1-2-2111111000000-2-22200000000000011-1-1
χ2522-2-222i−2i2-2-22i2i−2i−2i2-1-2-1121-20000-1-111−ii2i−2i−i−iii002-22i−2i000000000000-11−ii0000
χ2622-2-222i−2i2-2-22i2i−2i−2i2-1-2-1121-20000-1-111−ii2i−2i−i−iii00-22−2i2i0000000000001-1i−i0000
χ2722-2-222i−2i2-2-22i2i−2i−2i-1212-2-1-210000-1-1112i−2i−ii−i−iii0000002-22i−2i000000000000-11−ii
χ2822-2-222i−2i2-2-22i2i−2i−2i-1212-2-1-210000-1-1112i−2i−ii−i−iii000000-22−2i2i0000000000001-1i−i
χ2922-2-22−2i2i2-2-2−2i−2i2i2i2-1-2-1121-20000-1-111i−i−2i2iii−i−i002-2−2i2i000000000000-11i−i0000
χ3022-2-22−2i2i2-2-2−2i−2i2i2i2-1-2-1121-20000-1-111i−i−2i2iii−i−i00-222i−2i0000000000001-1−ii0000
χ3122-2-22−2i2i2-2-2−2i−2i2i2i-1212-2-1-210000-1-111−2i2ii−iii−i−i0000002-2−2i2i000000000000-11i−i
χ3222-2-22−2i2i2-2-2−2i−2i2i2i-1212-2-1-210000-1-111−2i2ii−iii−i−i000000-222i−2i0000000000001-1−ii
χ332-22-2200-22-20000222-2-2-22-22i−2i2i−2i2-22-200000000000000000000002i−2i2i−2i00000000
χ342-22-2200-22-20000222-2-2-22-2−2i2i−2i2i2-22-20000000000000000000000−2i2i−2i2i00000000
χ352-2-22200-2-22000022-2-22-2-222-2-222-2-2200000000000000000000002-2-2200000000
χ362-2-22200-2-22000022-2-22-2-22-222-22-2-220000000000000000000000-222-200000000
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
χ3944-4-444i−4i4-4-44i4i−4i−4i-2-22-22-222000011-1-1−2i2i−2i2iii−i−i00000000000000000000000000
χ4044-4-44−4i4i4-4-4−4i−4i4i4i-2-22-22-222000011-1-12i−2i2i−2i−i−iii00000000000000000000000000
χ414-44-4400-44-400004-2422-4-2-40000-22-220000000000000000000000000000000000
χ424-44-4400-44-40000-24-2-4-42420000-22-220000000000000000000000000000000000
χ434-44-4400-44-40000-2-2-2222-2200001-11-100003i−3i3i−3i00000000000000000000000000
χ444-44-4400-44-40000-2-2-2222-2200001-11-10000−3i3i−3i3i00000000000000000000000000
χ454-4-44400-4-4400004-2-42-2-4240000-222-20000000000000000000000000000000000
χ464-4-44400-4-440000-242-442-4-20000-222-20000000000000000000000000000000000
χ474-4-44400-4-440000-2-222-222-200001-1-1100003-3-3300000000000000000000000000
χ484-4-44400-4-440000-2-222-222-200001-1-110000-333-300000000000000000000000000
χ496666-366-3-3-3-3-3-3-30000000022220000000000002200000000-1-1-1-1-1-1-1-100000000
χ506666-366-3-3-3-3-3-3-300000000-2-2-2-2000000000000-2-2000000001111111100000000
χ516666-3-6-6-3-3-33333000000002222000000000000-2-2000000001111-1-1-1-100000000
χ526666-3-6-6-3-3-3333300000000-2-2-2-20000000000002200000000-1-1-1-1111100000000
χ5366-6-6-36i−6i-333−3i−3i3i3i000000002i2i−2i−2i0000000000002-200000000-1-111−i−iii00000000
χ5466-6-6-36i−6i-333−3i−3i3i3i00000000−2i−2i2i2i000000000000-220000000011-1-1ii−i−i00000000
χ5566-6-6-3−6i6i-3333i3i−3i−3i000000002i2i−2i−2i000000000000-220000000011-1-1−i−iii00000000
χ5666-6-6-3−6i6i-3333i3i−3i−3i00000000−2i−2i2i2i0000000000002-200000000-1-111ii−i−i00000000
χ576-66-6-3003-3333−3333−33000000002i−2i2i−2i0000000000000000000000−i3i3−i3i3−ii−ii00000000
χ586-66-6-3003-3333−3333−3300000000−2i2i−2i2i0000000000000000000000i3−i3i3−i3i−ii−i00000000
χ596-66-6-3003-33−3333−3333000000002i−2i2i−2i0000000000000000000000i3−i3i3−i3−ii−ii00000000
χ606-66-6-3003-33−3333−333300000000−2i2i−2i2i0000000000000000000000−i3i3−i3i3i−ii−i00000000
χ616-6-66-30033-3−3i33i33i3−3i3000000002-2-220000000000000000000000−i3i3i3−i3-111-100000000
χ626-6-66-30033-3−3i33i33i3−3i300000000-222-20000000000000000000000i3−i3−i3i31-1-1100000000
χ636-6-66-30033-33i3−3i3−3i33i3000000002-2-220000000000000000000000i3−i3−i3i3-111-100000000
χ646-6-66-30033-33i3−3i3−3i33i300000000-222-20000000000000000000000−i3i3i3−i31-1-1100000000

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