Finite Group Databasebeta

← Group #13148648

Character table — Group #13148648

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size11112222224444444466666666121212121212121218181818181818181818181818182424242424242424242436363636363636363636363636363636363636363672727272
order1222223666446612121212336666663666666622224444446666661212121212121212222444466666612121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11111-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-111-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1111111-1-1-1-11111-1-1-1-1
χ61111111111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1111-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-11-11-1-111111111-1-1-1-1-1-111
χ81111111111-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-11111111111-1-1
χ91111-1-111111-1-1-111-1-1111111111-1-1-1-1111111111-1-1111111-1-11-11-111-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-111-1
χ101111-1-111111-1-1-111-1-1111111111-1-1-1-111111-1-111-1-1-1-11111-1-11-11-111-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-11
χ111111-1-111111-1-1-111-1-1111111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-11-11-111-1-11-1-11-1111111-1-1-1-111-1-111-11-11
χ121111-1-111111-1-1-111-1-1111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-1111-11-1-111-1-111-1-11111-1-11-11-1
χ131111-1-11111-11-1-1-1-111111111111-1-1-1-11111111-1-111111111-1-1-11-11-1-111-1-11-1-1-11-1-111-1-1-1-11111-1-11-1-11
χ141111-1-11111-11-1-1-1-111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-11-11-1-111-11-1111-1-1-1-1-111-1-111-1-111-111-1
χ151111-1-11111-11-1-1-1-111111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-1111-11-111-11111-1-111-1-1-1-1111-11-1
χ161111-1-11111-11-1-1-1-111111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-11-11-1-11111-11-1-1111-1-11111-1-111-1-1-11-11
χ172222222222222222222-12-1-1-122-122-1-1-1-1-100220000000000-1-1-1-122-1-1-1-1022200000-1-1-1-100000000-1-100
χ182222222222222222222-12-1-1-122-122-1-1-1-1-100-2-20000000000-1-1-1-122-1-1-1-10-2-2-2000001111000000001100
χ19222222222222222222-12-1222-1-1-1-1-122-1-1-100000000220000-1-122-1-1-1-1-1-100002220000000000-1-1-1-100-1-1
χ20222222222222222222-12-1222-1-1-1-1-122-1-1-100000000-2-20000-1-122-1-1-1-1-1-10000-2-2-2000000000011110011
χ212222222222-2-222-2-2-2-22-12-1-1-122-122-1-1-1-1-100220000000000-1-111-2-2111102-2-200000-1-1-1-1000000001100
χ222222222222-2-222-2-2-2-22-12-1-1-122-122-1-1-1-1-100-2-20000000000-1-111-2-211110-22200000111100000000-1-100
χ232222222222-2-222-2-2-2-2-12-1222-1-1-1-1-122-1-1-100000000220000-1-1-2-21111110000-22-20000000000-1-1-1-10011
χ242222222222-2-222-2-2-2-2-12-1222-1-1-1-1-122-1-1-100000000-2-20000-1-1-2-211111100002-220000000000111100-1-1
χ252222-2-222222-2-2-222-2-22-12-1-1-122-1-2-211-1-1-10022000000000011-112-2-1-1110-2-2200000-1-111000000001-100
χ262222-2-222222-2-2-222-2-22-12-1-1-122-1-2-211-1-1-100-2-2000000000011-112-2-1-111022-20000011-1-100000000-1100
χ272222-2-222222-2-2-222-2-2-12-1222-1-1-111-2-2-1-1-100000000220000112-2-11-1-11100002-2-20000000000-1-11100-11
χ282222-2-222222-2-2-222-2-2-12-1222-1-1-111-2-2-1-1-100000000-2-20000112-2-11-1-1110000-222000000000011-1-1001-1
χ292222-2-22222-22-2-2-2-2222-12-1-1-122-1-2-211-1-1-100220000000000111-1-2211-1-10-22-200000-1-11100000000-1100
χ302222-2-22222-22-2-2-2-2222-12-1-1-122-1-2-211-1-1-100-2-20000000000111-1-2211-1-102-220000011-1-1000000001-100
χ312222-2-22222-22-2-2-2-222-12-1222-1-1-111-2-2-1-1-10000000022000011-221-111-1-10000-2-220000000000-1-111001-1
χ322222-2-22222-22-2-2-2-222-12-1222-1-1-111-2-2-1-1-100000000-2-2000011-221-111-1-1000022-2000000000011-1-100-11
χ3322-2-22-222-2-2002-20000222-2-22-2-222-22-22-2-200002i−2i2i−2i0000002-20000000000000000000002i−2i2i−2i00000000
χ3422-2-22-222-2-2002-20000222-2-22-2-222-22-22-2-20000−2i2i−2i2i0000002-2000000000000000000000−2i2i−2i2i00000000
χ3522-2-2-2222-2-200-220000222-2-22-2-22-22-222-2-200002i−2i−2i2i000000-220000000000000000000002i−2i−2i2i00000000
χ3622-2-2-2222-2-200-220000222-2-22-2-22-22-222-2-20000−2i2i2i−2i000000-22000000000000000000000−2i2i2i−2i00000000
χ372-2-22002-22-20000000022-22-2-2-2220000-22-22-22-200002-222-2-200000000000000000002-20000002-2000000
χ382-2-22002-22-20000000022-22-2-2-2220000-22-22-2-220000-2222-2-20000000000000000000-22000000-22000000
χ392-2-22002-22-20000000022-22-2-2-2220000-22-2-222-20000-22-2-22200000000000000000002-2000000-22000000
χ402-2-22002-22-20000000022-22-2-2-2220000-22-2-22-2200002-2-2-2220000000000000000000-220000002-2000000
χ41444444444444444444-2-2-2-2-2-2-2-21-2-2-2-21110000000000000011-2-2-2-211110000000000000000000000000
χ424444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-21-2-2-2-211100000000000000112222-1-1-1-10000000000000000000000000
χ434444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-21222211100000000000000-1-1-22-2211-1-10000000000000000000000000
χ444444-4-44444-44-4-4-4-444-2-2-2-2-2-2-2-21222211100000000000000-1-12-22-2-1-1110000000000000000000000000
χ4544-4-44-444-4-4004-400004-2422-2-4-4-24-4-22-22200000000000000-22000000000000000000000000000000000
χ4644-4-44-444-4-4004-40000-24-2-4-4422-2-224-4-22200000000000000-22000000000000000000000000000000000
χ4744-4-44-444-4-4004-40000-2-2-222-2221-22-221-1-1000000000000001-100003i−3i3i−3i0000000000000000000000000
χ4844-4-44-444-4-4004-40000-2-2-222-2221-22-221-1-1000000000000001-10000−3i3i−3i3i0000000000000000000000000
χ4944-4-4-4444-4-400-4400004-2422-2-4-4-2-442-2-222000000000000002-2000000000000000000000000000000000
χ5044-4-4-4444-4-400-440000-24-2-4-4422-22-2-44-222000000000000002-2000000000000000000000000000000000
χ5144-4-4-4444-4-400-440000-2-2-222-22212-22-21-1-100000000000000-1100003i−3i−3i3i0000000000000000000000000
χ5244-4-4-4444-4-400-440000-2-2-222-22212-22-21-1-100000000000000-110000−3i3i3i−3i0000000000000000000000000
χ534-44-4004-4-440000000044-4-44-44-440000-4-440000000000000000000000000000000000000000000000000
χ544-44-4004-4-44000000004-2-42-224-4-2000022-200000000000000000000000000000000000−2i32i3000000000000
χ554-44-4004-4-44000000004-2-42-224-4-2000022-2000000000000000000000000000000000002i3−2i3000000000000
χ564-44-4004-4-4400000000-242-44-4-22-2000022-2000000000000000000000000000000000000000000023−230000
χ574-44-4004-4-4400000000-242-44-4-22-2000022-20000000000000000000000000000000000000000000−23230000
χ584-4-44004-44-4000000004-2-4-222-44-200002-22004-400000000000000000000000000000-2200000000000000
χ594-4-44004-44-4000000004-2-4-222-44-200002-2200-44000000000000000000000000000002-200000000000000
χ604-4-44004-44-400000000-2424-4-42-2-200002-22000000004-40000000000000000000000000000000-22000000
χ614-4-44004-44-400000000-2424-4-42-2-200002-2200000000-4400000000000000000000000000000002-2000000
χ62666666-3-3-3-366-3-3-3-3-3-300000000000000002200222200-1-1-1-100000000002000000-1-10000-1-1-1-100000000
χ63666666-3-3-3-366-3-3-3-3-3-30000000000000000-2-200-2-2-2-20011110000000000-2000000110000111100000000
χ64666666-3-3-3-3-6-6-3-3333300000000000000002200-2-2-2-200-1-1-1-100000000002000000-1-10000111100000000
χ65666666-3-3-3-3-6-6-3-333330000000000000000-2-20022220011110000000000-2000000110000-1-1-1-100000000
χ666666-6-6-3-3-3-36-633-3-3330000000000000000220022-2-200-1-1-1-10000000000-2000000110000-1-11100000000
χ676666-6-6-3-3-3-36-633-3-3330000000000000000-2-200-2-22200111100000000002000000-1-1000011-1-100000000
χ686666-6-6-3-3-3-3-663333-3-300000000000000002200-2-22200-1-1-1-10000000000-200000011000011-1-100000000
χ696666-6-6-3-3-3-3-663333-3-30000000000000000-2-20022-2-200111100000000002000000-1-10000-1-11100000000
χ7066-6-66-6-3-33300-3333−3333−33000000000000000000002i−2i2i−2i00−i3i3−i3i300000000000000000−i3i30000−ii−ii00000000
χ7166-6-66-6-3-33300-3333−3333−3300000000000000000000−2i2i−2i2i00i3−i3i3−i300000000000000000i3−i30000i−ii−i00000000
χ7266-6-66-6-3-33300-33−3333−3333000000000000000000002i−2i2i−2i00i3−i3i3−i300000000000000000i3−i30000−ii−ii00000000
χ7366-6-66-6-3-33300-33−3333−333300000000000000000000−2i2i−2i2i00−i3i3−i3i300000000000000000−i3i30000i−ii−i00000000
χ7466-6-6-66-3-333003-333−33−3333000000000000000000002i−2i−2i2i00−i3i3−i3i300000000000000000i3−i30000−iii−i00000000
χ7566-6-6-66-3-333003-333−33−333300000000000000000000−2i2i2i−2i00i3−i3i3−i300000000000000000−i3i30000i−i−ii00000000
χ7666-6-6-66-3-333003-3−333333−33000000000000000000002i−2i−2i2i00i3−i3i3−i300000000000000000−i3i30000−iii−i00000000
χ7766-6-6-66-3-333003-3−333333−3300000000000000000000−2i2i2i−2i00−i3i3−i3i300000000000000000i3−i30000i−i−ii00000000
χ788-88-8008-8-8800000000-4-444-44-4420000-2-220000000000000000000000000000000000000000000000000
χ798-8-88008-88-800000000-4-44-4444-420000-22-20000000000000000000000000000000000000000000000000
χ8012-1212-1200-666-60000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000
χ8112-1212-1200-666-600000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000
χ8212-12-121200-66-660000000000000000000000004-400000000-2-22200000000000000000000000000000000000
χ8312-12-121200-66-66000000000000000000000000-440000000022-2-200000000000000000000000000000000000

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