Finite Group Databasebeta

← Group #13148565

Character table — Group #13148565

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order12222236664466336666661212366666661212121244444444441212121266121212121212244444412121212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-1111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-11
χ51111111111-1-11111111111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1-11-111111111-1-1-1-1-1-11-1-11
χ61111111111-1-11111111111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-11-1-11-1-1-1-11111-1-11111-111-1
χ71111111111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-111111-1-1-1-1111111-1-1-1-1
χ81111111111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ91111-1-111111-1-1-1111111111-11-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-1-11-1-111111-1-111-1-11111-1-1-11-11
χ101111-1-111111-1-1-1111111111-11-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11-111-1-11-1111-1-1-1-11111-1-111-1-1111-11-1
χ111111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-1111111111111-1-11-111-1-111-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1
χ121111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-111-1-111-1-11111-1-11-111-1-1-1-111-111-1-111-1-111-1-111-1-1-1-111
χ131111-1-11111-11-1-111111111-111-1-1-1-1111-1-11111-1-11111111111-1-1-11-1-111-1-1-11-11-111-1-111-1-1-1-1-1-111-1-111
χ141111-1-11111-11-1-111111111-111-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-1-11-1-111111-1-1-11-1-11111-1-1-1-111-1-111-1-1
χ151111-1-11111-11-1-111111111-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1111-1-1-1-1111111-1-11-11-1
χ161111-1-11111-11-1-111111111-111-1-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-11-1-111-111-111-1-1-111-1-11111-1-111-11-11
χ17222222222222222-1-1-1222-122-122-1-1-1-1-1222200000000220000-1-1-1-1-1-1-1-120000220000000000-1-1-1-1-100-1
χ18222222222222222-1-1-1222-122-122-1-1-1-1-1222200000000-2-20000-1-1-1-1-1-1-1-1-20000-2-2000000000011111001
χ1922222222222222-1222-1-1-1222-1-1-122-1-1-1-1-1-1-12222002200-1-1-1-1-1-122-1-1-1-100002000000-1-1-1-1-1-100000000
χ2022222222222222-1222-1-1-1222-1-1-122-1-1-1-1-1-1-1-2-2-2-200-2-2001111-1-122-1-1-1-10000-200000011111100000000
χ212222222222-2-2222-1-1-1222-1-2-2-122-1-1-1-1-1-2-2-2-200000000220000-1-1111111-20000-220000000000-1-1-1-11001
χ222222222222-2-2222-1-1-1222-1-2-2-122-1-1-1-1-1-2-2-2-200000000-2-20000-1-1111111200002-200000000001111-100-1
χ232222222222-2-222-1222-1-1-12-2-2-1-1-122-1-1-11111222200-2-2001111-1-1-2-211110000-2000000-1-1-1-11100000000
χ242222222222-2-222-1222-1-1-12-2-2-1-1-122-1-1-11111-2-2-2-2002200-1-1-1-1-1-1-2-21111000020000001111-1-100000000
χ252222-2-222222-2-2-22-1-1-1222-12-2-1-2-211-1-1-122-2-20000000022000011-11-1-11120000-2-2000000000011-1-1-1001
χ262222-2-222222-2-2-22-1-1-1222-12-2-1-2-211-1-1-122-2-200000000-2-2000011-11-1-111-20000220000000000-1-111100-1
χ272222-2-222222-2-2-2-1222-1-1-122-2-111-2-2-1-1-1-1-11122-2-200-2-2001111112-2-1-11100002000000-1-111-1-100000000
χ282222-2-222222-2-2-2-1222-1-1-122-2-111-2-2-1-1-1-1-111-2-222002200-1-1-1-1112-2-1-1110000-200000011-1-11100000000
χ292222-2-22222-22-2-22-1-1-1222-1-22-1-2-211-1-1-1-2-22200000000220000111-111-1-1-200002-2000000000011-1-1100-1
χ302222-2-22222-22-2-22-1-1-1222-1-22-1-2-211-1-1-1-2-22200000000-2-20000111-111-1-120000-220000000000-1-111-1001
χ312222-2-22222-22-2-2-1222-1-1-12-22-111-2-2-1-1-111-1-122-2-2002200-1-1-1-111-2211-1-10000-2000000-1-1111100000000
χ322222-2-22222-22-2-2-1222-1-1-12-22-111-2-2-1-1-111-1-1-2-22200-2-200111111-2211-1-10000200000011-1-1-1-100000000
χ332-22-2002-2-220000222-22-2-2-20020000-22-2000000002-22i−2i2i−2i2i2i−2i−2i0000000000000002-200000000002i−2i0000
χ342-22-2002-2-220000222-22-2-2-20020000-22-2000000002-2−2i2i−2i2i−2i−2i2i2i0000000000000002-20000000000−2i2i0000
χ352-22-2002-2-220000222-22-2-2-20020000-22-200000000-222i−2i−2i2i2i2i−2i−2i000000000000000-220000000000−2i2i0000
χ362-22-2002-2-220000222-22-2-2-20020000-22-200000000-22−2i2i2i−2i−2i−2i2i2i000000000000000-2200000000002i−2i0000
χ372-2-222-222-2-2002-222-2-2-2-2220022-22-22-2-200002i−2i2i−2i00000000002-2000000000000000002i−2i2i−2i0000000000
χ382-2-222-222-2-2002-222-2-2-2-2220022-22-22-2-20000−2i2i−2i2i00000000002-200000000000000000−2i2i−2i2i0000000000
χ392-2-222-222-2-2002-2-12-2-211-1200-1-112-2-1113−33−32i−2i2i−2i000000−i3i3−i3i3-11003−33−300000000000−ii−ii−i3i300000000
χ402-2-222-222-2-2002-2-12-2-211-1200-1-112-2-1113−33−3−2i2i−2i2i000000i3−i3i3−i3-11003−33−300000000000i−ii−ii3−i300000000
χ412-2-222-222-2-2002-2-12-2-211-1200-1-112-2-111−33−332i−2i2i−2i000000i3−i3i3−i3-1100−33−3300000000000−ii−iii3−i300000000
χ422-2-222-222-2-2002-2-12-2-211-1200-1-112-2-111−33−33−2i2i−2i2i000000−i3i3−i3i3-1100−33−3300000000000i−ii−i−i3i300000000
χ432-2-22-2222-2-200-2222-2-2-2-222002-22-222-2-200002i−2i−2i2i0000000000-22000000000000000002i−2i−2i2i0000000000
χ442-2-22-2222-2-200-2222-2-2-2-222002-22-222-2-20000−2i2i2i−2i0000000000-2200000000000000000−2i2i2i−2i0000000000
χ452-2-22-2222-2-200-22-12-2-211-1200-11-1-22-1113−3−332i−2i−2i2i000000i3−i3i3−i31-1003−3−3300000000000−iii−i−i3i300000000
χ462-2-22-2222-2-200-22-12-2-211-1200-11-1-22-1113−3−33−2i2i2i−2i000000−i3i3−i3i31-1003−3−3300000000000i−i−iii3−i300000000
χ472-2-22-2222-2-200-22-12-2-211-1200-11-1-22-111−333−32i−2i−2i2i000000−i3i3−i3i31-100−333−300000000000−iii−ii3−i300000000
χ482-2-22-2222-2-200-22-12-2-211-1200-11-1-22-111−333−3−2i2i2i−2i000000i3−i3i3−i31-100−333−300000000000i−i−ii−i3i300000000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111-2-2-2-20000000000000011-2-211110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-41-2-2-2-21112222000000000000001122-1-1-1-10000000000000000000000000
χ514444-4-444444-4-4-4-2-2-2-2-2-2-2-24-412222111-2-22200000000000000-1-1-2211-1-10000000000000000000000000
χ524444-4-44444-44-4-4-2-2-2-2-2-2-2-2-441222211122-2-200000000000000-1-12-2-1-1110000000000000000000000000
χ5344-4-4004-44-4000044-44-44-4-40040000-4-44000000000000000000000000000000000000000000000000000
χ5444-4-4004-44-400004-22-2-44-4200-2000022-2000000000000000000000000000000000000000000023−23000000
χ5544-4-4004-44-400004-22-2-44-4200-2000022-20000000000000000000000000000000000000000000−2323000000
χ5644-4-4004-44-40000-24-442-22-400-2000022-20000000000000023−23−2323000000000000000000000000000000000
χ5744-4-4004-44-40000-24-442-22-400-2000022-200000000000000−232323−23000000000000000000000000000000000
χ584-44-4004-4-4400004-2-224-4-4200-200002-220000000000004i−4i0000000000000000000000000000000−2i2i0000
χ594-44-4004-4-4400004-2-224-4-4200-200002-22000000000000−4i4i00000000000000000000000000000002i−2i0000
χ604-44-4004-4-440000-244-4-222-400-200002-2200000000004i−4i00−2i−2i2i2i000000000000000000000000000000000
χ614-44-4004-4-440000-244-4-222-400-200002-220000000000−4i4i002i2i−2i−2i000000000000000000000000000000000
χ624-4-444-444-4-4004-44-222-4-44-200-24-4-22-222000000000000000000-220000000000000000000000000000000
χ634-4-444-444-4-4004-4-2-22222-2-2001-22-221-1-123−2323−23000000000000001-100−33−330000000000000000000000000
χ644-4-444-444-4-4004-4-2-22222-2-2001-22-221-1-1−2323−2323000000000000001-1003−33−30000000000000000000000000
χ654-4-44-4444-4-400-444-222-4-44-200-2-442-2-2220000000000000000002-20000000000000000000000000000000
χ664-4-44-4444-4-400-44-2-22222-2-20012-22-21-1-123−23−232300000000000000-1100−333−30000000000000000000000000
χ674-4-44-4444-4-400-44-2-22222-2-20012-22-21-1-1−232323−2300000000000000-11003−3−330000000000000000000000000
χ68666666-3-3-3-366-3-300000000-3-300000000000000002200000000000000000222000-1-1-1-100000000000-1-10
χ69666666-3-3-3-366-3-300000000-3-30000000000000000-2-200000000000000000-2-2-2000111100000000000110
χ70666666-3-3-3-3-6-6-3-3000000003300000000000000002200000000000000000-22-2000-1-1-1-100000000000110
χ71666666-3-3-3-3-6-6-3-300000000330000000000000000-2-2000000000000000002-22000111100000000000-1-10
χ726666-6-6-3-3-3-36-63300000000-33000000000000000022000000000000000002-2-2000-1-11100000000000-110
χ736666-6-6-3-3-3-36-63300000000-330000000000000000-2-200000000000000000-22200011-1-1000000000001-10
χ746666-6-6-3-3-3-3-6633000000003-300000000000000002200000000000000000-2-22000-1-111000000000001-10
χ756666-6-6-3-3-3-3-6633000000003-30000000000000000-2-20000000000000000022-200011-1-100000000000-110
χ7688-8-8008-88-80000-4-44-44-4440020000-2-22000000000000000000000000000000000000000000000000000
χ778-88-8008-8-880000-4-4-44-44440020000-22-2000000000000000000000000000000000000000000000000000
χ781212-12-1200-66-6600000000000000000000000000000000000000000000000000000000023−2300000000000000
χ791212-12-1200-66-66000000000000000000000000000000000000000000000000000000000−232300000000000000
χ8012-1212-1200-666-60000000000000000000000000000004-400000000000000000000000-220000000000000000
χ8112-1212-1200-666-6000000000000000000000000000000-44000000000000000000000002-20000000000000000
χ8212-12-121212-12-6-66600-66000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-1212-6-666006-6000000000000000000000000000000000000000000000000000000000000000000000

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