Finite Group Databasebeta

← Group #11721315

Character table — Group #11721315

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111122222222226666666699991212121212121212121212121818181818181818181818181818181818183636363636363636
order122222366666663366666644443666666666662244444444121212121212121266121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-1111-1-1-1-111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ61111-1-1111-1-1-1-111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111-1-1111-1-1-1-1111111111-1-1-1-11-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ81111-1-1111-1-1-1-1111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1
χ911-1-11-111-111-1-1-1111-1-1-1-11ii−i−i11-11-11-1-111-1-11-11-1i−ii−ii−iii−i−iii−i−i1-11-1i−ii−i
χ1011-1-11-111-111-1-1-1111-1-1-1-11ii−i−i11-11-11-1-111-1-1-11-11−iii−i−iiii−i−iii−i−i-11-11−ii−ii
χ1111-1-11-111-111-1-1-1111-1-1-1-11−i−iii11-11-11-1-111-1-11-11-1−ii−ii−ii−i−iii−i−iii1-11-1−ii−ii
χ1211-1-11-111-111-1-1-1111-1-1-1-11−i−iii11-11-11-1-111-1-1-11-11i−i−iii−i−i−iii−i−iii-11-11i−ii−i
χ1311-1-1-1111-1-1-111-1111-1-1-1-11ii−i−i1-11-111-1-1-1-1111-1-11−ii−iii−iii−i−i−i−iii1-1-11i−i−ii
χ1411-1-1-1111-1-1-111-1111-1-1-1-11ii−i−i1-11-111-1-1-1-111-111-1i−i−ii−iiii−i−i−i−iii-111-1−iii−i
χ1511-1-1-1111-1-1-111-1111-1-1-1-11−i−iii1-11-111-1-1-1-1111-1-11i−ii−i−ii−i−iiiii−i−i1-1-11−iii−i
χ1611-1-1-1111-1-1-111-1111-1-1-1-11−i−iii1-11-111-1-1-1-111-111-1−iii−ii−i−i−iiiii−i−i-111-1i−i−ii
χ17222222222222222-12-1-122-10000-122-1-1-1-1-1-1-1-1-1222200000000000000-1-1-1-10000
χ18222222222222222-12-1-122-10000-122-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000011110000
χ1922222222222222-12-122-1-120000-1-1-122-1-1-1-1-1-1-10000220022000000000000-1-1-1-1
χ2022222222222222-12-122-1-120000-1-1-122-1-1-1-1-1-1-10000-2-200-2-20000000000001111
χ212222-2-2222-2-2-2-222-12-1-122-10000-1-2-211-1-1-1111122-2-200000000000000-1-1110000
χ222222-2-2222-2-2-2-222-12-1-122-10000-1-2-211-1-1-11111-2-2220000000000000011-1-10000
χ232222-2-2222-2-2-2-22-12-122-1-120000-111-2-2-1-1-1111100002200-2-200000000000011-1-1
χ242222-2-2222-2-2-2-22-12-122-1-120000-111-2-2-1-1-111110000-2-20022000000000000-1-111
χ2522-2-22-222-222-2-2-22-1211-2-2-10000-12-2-11-111-1-1112-22-200000000000000-11-110000
χ2622-2-22-222-222-2-2-22-1211-2-2-10000-12-2-11-111-1-111-22-22000000000000001-11-10000
χ2722-2-22-222-222-2-2-2-12-1-2-21120000-1-112-2-111-1-11100002i−2i002i−2i000000000000−ii−ii
χ2822-2-22-222-222-2-2-2-12-1-2-21120000-1-112-2-111-1-1110000−2i2i00−2i2i000000000000i−ii−i
χ2922-2-2-2222-2-2-222-22-1211-2-2-10000-1-221-1-11111-1-12-2-2200000000000000-111-10000
χ3022-2-2-2222-2-2-222-22-1211-2-2-10000-1-221-1-11111-1-1-222-2000000000000001-1-110000
χ3122-2-2-2222-2-2-222-2-12-1-2-21120000-11-1-22-11111-1-100002i−2i00−2i2i000000000000i−i−ii
χ3222-2-2-2222-2-2-222-2-12-1-2-21120000-11-1-22-11111-1-10000−2i2i002i−2i000000000000−iii−i
χ332-22-2002-220000-222-22-22-2-22i−2i2i−2i20000-22-2000000000000002i−2i2i−2i000000000000
χ342-22-2002-220000-222-22-22-2-2−2i2i−2i2i20000-22-200000000000000−2i2i−2i2i000000000000
χ352-2-22002-2-20000222-2-22-22-22-2-2220000-2-22000000000000002-2-22000000000000
χ362-2-22002-2-20000222-2-22-22-2-222-220000-2-2200000000000000-222-2000000000000
χ3744444444444444-2-2-2-2-2-2-2-200001-2-2-2-2111111100000000000000000000000000
χ384444-4-4444-4-4-4-44-2-2-2-2-2-2-2-2000012222111-1-1-1-100000000000000000000000000
χ3944-4-44-444-444-4-4-4-2-2-22222-200001-22-221-1-111-1-100000000000000000000000000
χ4044-4-4-4444-4-4-444-4-2-2-22222-2000012-22-21-1-1-1-11100000000000000000000000000
χ414-44-4004-440000-44-2-4-224-420000-200002-22000000000000000000000000000000
χ424-44-4004-440000-4-2424-4-22-40000-200002-22000000000000000000000000000000
χ434-44-4004-440000-4-2-22-22-222000010000-11-13-33-300000000000000000000000000
χ444-44-4004-440000-4-2-22-22-222000010000-11-1-33-3300000000000000000000000000
χ454-4-44004-4-4000044-2-42-2-4420000-2000022-2000000000000000000000000000000
χ464-4-44004-4-400004-242-442-2-40000-2000022-2000000000000000000000000000000
χ474-4-44004-4-400004-2-222-22-22000010000-1-113-3-3300000000000000000000000000
χ484-4-44004-4-400004-2-222-22-22000010000-1-11-333-300000000000000000000000000
χ49666666-3-3-3-3-3-3-3-30000000022220000000000000000002200-1-1-1-1-1-1-1-100000000
χ50666666-3-3-3-3-3-3-3-300000000-2-2-2-2000000000000000000-2-2001111111100000000
χ516666-6-6-3-3-33333-3000000002222000000000000000000-2-200-1-1-1-1111100000000
χ526666-6-6-3-3-33333-300000000-2-2-2-200000000000000000022001111-1-1-1-100000000
χ5366-6-66-6-3-33-3-3333000000002i2i−2i−2i0000000000000000002i−2i00−i−iii−i−iii00000000
χ5466-6-66-6-3-33-3-333300000000−2i−2i2i2i000000000000000000−2i2i00ii−i−iii−i−i00000000
χ5566-6-6-66-3-3333-3-33000000002i2i−2i−2i000000000000000000−2i2i00−i−iiiii−i−i00000000
χ5666-6-6-66-3-3333-3-3300000000−2i−2i2i2i0000000000000000002i−2i00ii−i−i−i−iii00000000
χ576-66-600-33-3−3i33i3−3i33i33000000002i−2i2i−2i0000000000000000000000−ii−ii3−33−300000000
χ586-66-600-33-3−3i33i3−3i33i3300000000−2i2i−2i2i0000000000000000000000i−ii−i−33−3300000000
χ596-66-600-33-33i3−3i33i3−3i33000000002i−2i2i−2i0000000000000000000000−ii−ii−33−3300000000
χ606-66-600-33-33i3−3i33i3−3i3300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−300000000
χ616-6-6600-333−3i33i33i3−3i3-3000000002-2-220000000000000000000000-111-1−i3i3i3−i300000000
χ626-6-6600-333−3i33i33i3−3i3-300000000-222-200000000000000000000001-1-11i3−i3−i3i300000000
χ636-6-6600-3333i3−3i3−3i33i3-3000000002-2-220000000000000000000000-111-1i3−i3−i3i300000000
χ646-6-6600-3333i3−3i3−3i33i3-300000000-222-200000000000000000000001-1-11−i3i3i3−i300000000

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