Finite Group Databasebeta

← Group #11721136

Character table — Group #11721136

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111122222222226666666699991212121212121212121212121818181818181818181818181818181818183636363636363636
order1222344666121212123366666644443666121212121212121222224444441212121212121212666612121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111
χ711111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-111
χ811111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1
χ911-1-111-11-1-111-1-111-1-1-111-1ii−i−i1-1-1111-1-111-1-11-11-1i−ii−ii−iii−i−iii−i−i1-11-1i−ii−i
χ1011-1-111-11-1-111-1-111-1-1-111-1ii−i−i1-1-1111-1-111-1-1-11-11i−i−ii−iiii−i−iii−i−i-11-11−ii−ii
χ1111-1-111-11-1-111-1-111-1-1-111-1−i−iii1-1-1111-1-111-1-11-11-1−ii−ii−ii−i−iii−i−iii1-11-1−ii−ii
χ1211-1-111-11-1-111-1-111-1-1-111-1−i−iii1-1-1111-1-111-1-1-11-11−iii−ii−i−i−iii−i−iii-11-11i−ii−i
χ1311-1-11-111-1-1-1-11111-1-1-111-1ii−i−i1-1-11-1-111-1-1111-1-11−iii−i−iiii−i−i−i−iii1-1-11i−i−ii
χ1411-1-11-111-1-1-1-11111-1-1-111-1ii−i−i1-1-11-1-111-1-111-111-1−ii−iii−iii−i−i−i−iii-111-1−iii−i
χ1511-1-11-111-1-1-1-11111-1-1-111-1−i−iii1-1-11-1-111-1-1111-1-11i−i−iii−i−i−iiiii−i−i1-1-11−iii−i
χ1611-1-11-111-1-1-1-11111-1-1-111-1−i−iii1-1-11-1-111-1-111-111-1i−ii−i−ii−i−iiiii−i−i-111-1i−i−ii
χ17222222222222222-12-1-12-120000-1-1-1-12-12-1-1-1-1-1222200000000000000-1-1-1-10000
χ18222222222222222-12-1-12-120000-1-1-1-12-12-1-1-1-1-1-2-2-2-20000000000000011110000
χ1922222222222222-12-122-12-10000-1-1-1-1-12-12-1-1-1-10000002222000000000000-1-1-1-1
χ2022222222222222-12-122-12-10000-1-1-1-1-12-12-1-1-1-1000000-2-2-2-20000000000001111
χ2122222-2-2222-2-2-2-22-12-1-12-120000-1-1-1-1-21-21111122-2-200000000000000-1-1110000
χ2222222-2-2222-2-2-2-22-12-1-12-120000-1-1-1-1-21-211111-2-2220000000000000011-1-10000
χ2322222-2-2222-2-2-2-2-12-122-12-10000-1-1-1-11-21-2111100000022-2-2000000000000-1-111
χ2422222-2-2222-2-2-2-2-12-122-12-10000-1-1-1-11-21-21111000000-2-22200000000000011-1-1
χ2522-2-222-22-2-222-2-22-1-2112-1-20000-111-12-1-21-1-1112-22-200000000000000-11-110000
χ2622-2-222-22-2-222-2-22-1-2112-1-20000-111-12-1-21-1-111-22-22000000000000001-11-10000
χ2722-2-222-22-2-222-2-2-121-2-2-1210000-111-1-121-2-1-1110000002i−2i2i−2i000000000000−ii−ii
χ2822-2-222-22-2-222-2-2-121-2-2-1210000-111-1-121-2-1-111000000−2i2i−2i2i000000000000i−ii−i
χ2922-2-22-222-2-2-2-2222-1-2112-1-20000-111-1-212-111-1-12-2-2200000000000000-111-10000
χ3022-2-22-222-2-2-2-2222-1-2112-1-20000-111-1-212-111-1-1-222-2000000000000001-1-110000
χ3122-2-22-222-2-2-2-222-121-2-2-1210000-111-11-2-1211-1-10000002i−2i−2i2i000000000000−iii−i
χ3222-2-22-222-2-2-2-222-121-2-2-1210000-111-11-2-1211-1-1000000−2i2i2i−2i000000000000i−i−ii
χ332-22-2200-22-200002222-2-2-2-22i−2i2i−2i22-2-20000000000000000002i−2i2i−2i000000000000
χ342-22-2200-22-200002222-2-2-2-2−2i2i−2i2i22-2-2000000000000000000−2i2i−2i2i000000000000
χ352-2-22200-2-22000022-2-22-2-222-2-222-22-20000000000000000002-2-22000000000000
χ362-2-22200-2-22000022-2-22-2-22-222-22-22-2000000000000000000-222-2000000000000
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
χ3944-4-444-44-4-444-4-4-2-2222-2-2200001-1-11-2-22211-1-100000000000000000000000000
χ4044-4-44-444-4-4-4-444-2-2222-2-2200001-1-1122-2-2-1-11100000000000000000000000000
χ414-44-4400-44-400004-24-22-42-40000-2-2220000000000000000000000000000000000
χ424-44-4400-44-40000-24-24-42-420000-2-2220000000000000000000000000000000000
χ434-44-4400-44-40000-2-2-2-22222000011-1-100003i−3i3i−3i00000000000000000000000000
χ444-44-4400-44-40000-2-2-2-22222000011-1-10000−3i3i−3i3i00000000000000000000000000
χ454-4-44400-4-4400004-2-42-2-4240000-22-220000000000000000000000000000000000
χ464-4-44400-4-440000-242-442-4-20000-22-220000000000000000000000000000000000
χ474-4-44400-4-440000-2-222-222-200001-11-100003i−3i−3i3i00000000000000000000000000
χ484-4-44400-4-440000-2-222-222-200001-11-10000−3i3i3i−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
χ5366-6-6-36-6-333-3-333000000002i2i−2i−2i00000000000000002i−2i0000−i−iii−i−iii00000000
χ5466-6-6-36-6-333-3-33300000000−2i−2i2i2i0000000000000000−2i2i0000ii−i−iii−i−i00000000
χ5566-6-6-3-66-33333-3-3000000002i2i−2i−2i0000000000000000−2i2i0000−i−iiiii−i−i00000000
χ5666-6-6-3-66-33333-3-300000000−2i−2i2i2i00000000000000002i−2i0000ii−i−i−i−iii00000000
χ576-66-6-3003-3333−3333−33000000002i−2i2i−2i0000000000000000000000−ii−ii−i3i3−i3i300000000
χ586-66-6-3003-3333−3333−3300000000−2i2i−2i2i0000000000000000000000i−ii−ii3−i3i3−i300000000
χ596-66-6-3003-33−3333−3333000000002i−2i2i−2i0000000000000000000000−ii−iii3−i3i3−i300000000
χ606-66-6-3003-33−3333−333300000000−2i2i−2i2i0000000000000000000000i−ii−i−i3i3−i3i300000000
χ616-6-66-30033-333−33−3333000000002-2-220000000000000000000000-111-1−333−300000000
χ626-6-66-30033-333−33−333300000000-222-200000000000000000000001-1-113−3−3300000000
χ636-6-66-30033-3−333333−33000000002-2-220000000000000000000000-111-13−3−3300000000
χ646-6-66-30033-3−333333−3300000000-222-200000000000000000000001-1-11−333−300000000

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