Finite Group Databasebeta

← Group #13148643

Character table — Group #13148643

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order1222223666446633666666121236666666121212122222444444666666121212121212222444466666612121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111-1-11111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11111111111-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-11-1111111-1-1-1-11111-1-1-1-1
χ61111111111-1-11111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1111-11-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-11-111111-1-11111-1-1-1-1-1-111
χ81111111111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-11111111111-1-1
χ91111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1111111-1-1111111-1-11-111-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-111-1
χ101111-1-111111-1-1-1111111111-11-1-1-1-111111-1-111-1-111-1-1-1-11111-1-11-111-1-1-111-1-111-1-111-1-111-1-1-1-1111-1-11
χ111111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-111-1-11-1-11-11111-1-111-1-111-1-111-11-11
χ121111-1-111111-1-1-1111111111-11-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1111-11-1-1-1-11111-1-11111-1-11-11-1
χ131111-1-11111-11-1-111111111-111-1-1-1-1111-1-1111111-1-111111111-1-1-11-1-111-1-11-1-1-1111-1-1-1-1-1-11111-1-11-1-11
χ141111-1-11111-11-1-111111111-111-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-1-11-1-111-11-1111-1-1-111-1-1-1-111-1-111-111-1
χ151111-1-11111-11-1-111111111-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1111-11-111-111-1-11111-1-1-1-1111-11-1
χ161111-1-11111-11-1-111111111-111-1-1-1-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-11-1-11111-11-1-11-1-1111111-1-111-1-1-11-11
χ17222222222222222-12-12-1-1222-122-1-1-1-1-1-1-1-1-12200222200-1-1-1-1-1-122-1-1-1-120000000000-1-1-1-1-1-100000000
χ18222222222222222-12-12-1-1222-122-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2001111-1-122-1-1-1-1-2000000000011111100000000
χ1922222222222222-12-12-122-122-1-1-122-1-1-1222200000000220000-1-1-1-1-1-1-1-100002220000000000-1-1-1-100-1-1
χ2022222222222222-12-12-122-122-1-1-122-1-1-1222200000000-2-20000-1-1-1-1-1-1-1-10000-2-2-2000000000011110011
χ212222222222-2-2222-12-12-1-12-2-2-122-1-1-1-1-111112200-2-2-2-200-1-1-1-1-1-1-2-2111120000000000-1-1111100000000
χ222222222222-2-2222-12-12-1-12-2-2-122-1-1-1-1-11111-2-2002222001111-1-1-2-21111-2000000000011-1-1-1-100000000
χ232222222222-2-222-12-12-122-1-2-2-1-1-122-1-1-1-2-2-2-200000000220000-1-11111110000-22-20000000000-1-1-1-10011
χ242222222222-2-222-12-12-122-1-2-2-1-1-122-1-1-1-2-2-2-200000000-2-20000-1-111111100002-220000000000111100-1-1
χ252222-2-222222-2-2-22-12-12-1-122-2-1-2-211-1-1-1-1-111220022-2-200-1-1-1-1112-2-1-111-2000000000011-1-11100000000
χ262222-2-222222-2-2-22-12-12-1-122-2-1-2-211-1-1-1-1-111-2-200-2-222001111112-2-1-11120000000000-1-111-1-100000000
χ272222-2-222222-2-2-2-12-12-122-12-2-111-2-2-1-1-122-2-20000000022000011-11-1-11100002-2-20000000000-1-11100-11
χ282222-2-222222-2-2-2-12-12-122-12-2-111-2-2-1-1-122-2-200000000-2-2000011-11-1-1110000-222000000000011-1-1001-1
χ292222-2-22222-22-2-22-12-12-1-12-22-1-2-211-1-1-111-1-12200-2-22200-1-1-1-111-2211-1-1-200000000001111-1-100000000
χ302222-2-22222-22-2-22-12-12-1-12-22-1-2-211-1-1-111-1-1-2-20022-2-200111111-2211-1-120000000000-1-1-1-11100000000
χ312222-2-22222-22-2-2-12-12-122-1-22-111-2-2-1-1-1-2-22200000000220000111-111-1-10000-2-220000000000-1-111001-1
χ322222-2-22222-22-2-2-12-12-122-1-22-111-2-2-1-1-1-2-22200000000-2-20000111-111-1-1000022-2000000000011-1-100-11
χ3322-2-22-22-2-22002-22222-2-2-2-20022-22-22-2-2000000002i−2i2i−2i0000002-200000000000000000002i−2i2i−2i00000000
χ3422-2-22-22-2-22002-22222-2-2-2-20022-22-22-2-200000000−2i2i−2i2i0000002-20000000000000000000−2i2i−2i2i00000000
χ3522-2-22-22-2-22002-22-12-1-211-200-12-2-11-1113−33−300002i−2i2i−2i00−i3−i3i3i3-11003−33−300000000000−i3i3−ii−ii00000000
χ3622-2-22-22-2-22002-22-12-1-211-200-12-2-11-1113−33−30000−2i2i−2i2i00i3i3−i3−i3-11003−33−300000000000i3−i3i−ii−i00000000
χ3722-2-22-22-2-22002-22-12-1-211-200-12-2-11-111−33−3300002i−2i2i−2i00i3i3−i3−i3-1100−33−3300000000000i3−i3−ii−ii00000000
χ3822-2-22-22-2-22002-22-12-1-211-200-12-2-11-111−33−330000−2i2i−2i2i00−i3−i3i3i3-1100−33−3300000000000−i3i3i−ii−i00000000
χ3922-2-2-222-2-2200-222222-2-2-2-2002-22-222-2-2000000002i−2i−2i2i000000-2200000000000000000002i−2i−2i2i00000000
χ4022-2-2-222-2-2200-222222-2-2-2-2002-22-222-2-200000000−2i2i2i−2i000000-220000000000000000000−2i2i2i−2i00000000
χ4122-2-2-222-2-2200-222-12-1-211-200-1-221-1-1113−3−3300002i−2i−2i2i00−i3−i3i3i31-1003−3−3300000000000i3−i3−iii−i00000000
χ4222-2-2-222-2-2200-222-12-1-211-200-1-221-1-1113−3−330000−2i2i2i−2i00i3i3−i3−i31-1003−3−3300000000000−i3i3i−i−ii00000000
χ4322-2-2-222-2-2200-222-12-1-211-200-1-221-1-111−333−300002i−2i−2i2i00i3i3−i3−i31-100−333−300000000000−i3i3−iii−i00000000
χ4422-2-2-222-2-2200-222-12-1-211-200-1-221-1-111−333−30000−2i2i2i−2i00−i3−i3i3i31-100−333−300000000000i3−i3i−i−ii00000000
χ452-2-220022-2-2000022-2-2-22-220020000-22-200002-22-200002-22-22-20000000000000002-2000000002-2000000
χ462-2-220022-2-2000022-2-2-22-220020000-22-200002-2-220000-222-22-2000000000000000-2200000000-22000000
χ472-2-220022-2-2000022-2-2-22-220020000-22-20000-222-20000-22-22-220000000000000002-200000000-22000000
χ482-2-220022-2-2000022-2-2-22-220020000-22-20000-22-2200002-2-22-22000000000000000-22000000002-2000000
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
χ5344-4-44-44-4-44004-4-24-242-4-4200-2-224-4-222000000000000000000-220000000000000000000000000000000
χ5444-4-44-44-4-44004-4-2-2-2-22222001-22-221-1-123−2323−23000000000000001-100−33−330000000000000000000000000
χ5544-4-44-44-4-44004-4-2-2-2-22222001-22-221-1-1−2323−2323000000000000001-1003−33−30000000000000000000000000
χ5644-4-4-444-4-4400-44-24-242-4-4200-22-2-44-2220000000000000000002-20000000000000000000000000000000
χ5744-4-4-444-4-4400-44-2-2-2-222220012-22-21-1-123−23−232300000000000000-1100−333−30000000000000000000000000
χ5844-4-4-444-4-4400-44-2-2-2-222220012-22-21-1-1−232323−2300000000000000-11003−3−330000000000000000000000000
χ594-44-4004-44-4000044-4-44-44-40040000-4-44000000000000000000000000000000000000000000000000000
χ604-44-4004-44-400004-2-4242-2-400-2000022-200000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ614-44-4004-44-400004-2-4242-2-400-2000022-2000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ624-44-4004-44-40000-242-4-2-44200-2000022-200000000000000000000000000000000000000000000023−230000
χ634-44-4004-44-40000-242-4-2-44200-2000022-2000000000000000000000000000000000000000000000−23230000
χ644-4-440044-4-400004-2-42-4-22400-200002-2200004-400000000-22-22000000000000000000000000000000000
χ654-4-440044-4-400004-2-42-4-22400-200002-220000-44000000002-22-2000000000000000000000000000000000
χ664-4-440044-4-40000-242-424-4-200-200002-220000000000004-400000000000000000000000000000-22000000
χ674-4-440044-4-40000-242-424-4-200-200002-22000000000000-44000000000000000000000000000002-2000000
χ68666666-3-3-3-366-3-300000000-3-300000000000000220000000000000000000222000-1-1-1-10000000000-1-100
χ69666666-3-3-3-366-3-300000000-3-300000000000000-2-20000000000000000000-2-2-2000111100000000001100
χ70666666-3-3-3-3-6-6-3-30000000033000000000000002200000000000000000002-2-2000-1-1-1-100000000001100
χ71666666-3-3-3-3-6-6-3-3000000003300000000000000-2-20000000000000000000-22200011110000000000-1-100
χ726666-6-6-3-3-3-36-63300000000-3300000000000000220000000000000000000-2-22000-1-11100000000001-100
χ736666-6-6-3-3-3-36-63300000000-3300000000000000-2-2000000000000000000022-200011-1-10000000000-1100
χ746666-6-6-3-3-3-3-6633000000003-300000000000000220000000000000000000-22-2000-1-1110000000000-1100
χ756666-6-6-3-3-3-3-6633000000003-300000000000000-2-200000000000000000002-2200011-1-100000000001-100
χ768-88-8008-88-80000-4-444-44-440020000-2-22000000000000000000000000000000000000000000000000000
χ778-8-880088-8-80000-4-4444-44-40020000-22-2000000000000000000000000000000000000000000000000000
χ781212-12-1212-12-666-600-66000000000000000000000000000000000000000000000000000000000000000000000
χ791212-12-12-1212-666-6006-6000000000000000000000000000000000000000000000000000000000000000000000
χ8012-1212-1200-66-66000000000000000000000000000000000000000000000000000000000−2i32i300000000000000
χ8112-1212-1200-66-660000000000000000000000000000000000000000000000000000000002i3−2i300000000000000
χ8212-12-121200-6-66600000000000000000000000000004-40000000000000000000000000-220000000000000000
χ8312-12-121200-6-6660000000000000000000000000000-4400000000000000000000000002-20000000000000000

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