Finite Group Databasebeta

← Group #13137888

Character table — Group #13137888

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222224466666666888121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order1222344666121233666666412123666121212121212121212121212121244888812121212242424242424242422466661212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111
χ311111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-1-111-1-1
χ511111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-11111-1-1
χ711111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1111-1-111
χ92222222222222-12-12-12-1222-1-1-1-12-12-122-1-1-1-1-1-1-1-100002200000000-1-1-1-102000-1-100
χ102222222222222-12-12-12-1222-1-1-1-12-12-122-1-1-1-1-1-1-1-10000-2-20000000011110-20001100
χ112222222222222-12-12-12-1-2-2-2-1-1-1-12-12-1-2-211-1-1111100002200000000-1-1-1-10-20001100
χ122222222222222-12-12-12-1-2-2-2-1-1-1-12-12-1-2-211-1-111110000-2-200000000111102000-1-100
χ13222222222222-12-12-12-12222-1-1-1-1-12-12-1-122-1-1-1-1-1-10022000000-1-1-1-10000200-1-10000
χ14222222222222-12-12-12-12222-1-1-1-1-12-12-1-122-1-1-1-1-1-100-2-200000011110000-200110000
χ15222222222222-12-12-12-12-2-2-2-1-1-1-1-12-1211-2-2-1-111110022000000-1-1-1-10000-200110000
χ16222222222222-12-12-12-12-2-2-2-1-1-1-1-12-1211-2-2-1-1111100-2-200000011110000200-1-10000
χ1722222-2-2222-2-2222222220002222-2-2-2-20000-2-200002-2000022-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-20000-2-20000-220000-2-22200000000000000000
χ1922-2-222-22-2-22-222-2-222-2-20002-22-22-2-2200002-20000002i−2i0000002i2i−2i−2i0000000000000
χ2022-2-222-22-2-22-222-2-222-2-20002-22-22-2-2200002-2000000−2i2i000000−2i−2i2i2i0000000000000
χ2122-2-222-22-2-22-2-121-2-121-2000-11-11-1-2123−300-1133−3−3002i−2i000000−i−iii0000000−i3i30000
χ2222-2-222-22-2-22-2-121-2-121-2000-11-11-1-2123−300-1133−3−300−2i2i000000ii−i−i0000000i3−i30000
χ2322-2-222-22-2-22-2-121-2-121-2000-11-11-1-212−3300-11−3−333002i−2i000000−i−iii0000000i3−i30000
χ2422-2-222-22-2-22-2-121-2-121-2000-11-11-1-212−3300-11−3−33300−2i2i000000ii−i−i0000000−i3i30000
χ2522-2-22-222-2-2-2222-2-222-2-20002-22-2-222-20000-22000000002i−2i000000002i2i−2i−2i000000000
χ2622-2-22-222-2-2-2222-2-222-2-20002-22-2-222-20000-2200000000−2i2i00000000−2i−2i2i2i000000000
χ2722-2-22-222-2-2-222-1-212-1-21000-11-11-2-121003−31-13−33−300002i−2i00000000−i−iii00000−i3i300
χ2822-2-22-222-2-2-222-1-212-1-21000-11-11-2-121003−31-13−33−30000−2i2i00000000ii−i−i00000i3−i300
χ2922-2-22-222-2-2-222-1-212-1-21000-11-11-2-12100−331-1−33−3300002i−2i00000000−i−iii00000i3−i300
χ3022-2-22-222-2-2-222-1-212-1-21000-11-11-2-12100−331-1−33−330000−2i2i00000000ii−i−i00000−i3i300
χ31444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ32444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2222211-1-1-1-1000000000000000000000000000
χ3344444-4-4444-4-44-24-24-24-2000-2-2-2-2-42-420000220000000000000000000000000000000
χ3444444-4-4444-4-4-24-24-24-24000-2-2-2-22-42-40000220000000000000000000000000000000
χ3544444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000-1-13-3-33000000000000000000000000000
χ3644444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000-1-1-333-3000000000000000000000000000
χ3744-4-444-44-4-44-44-2-424-2-42000-22-2242-4-20000-220000000000000000000000000000000
χ3844-4-444-44-4-44-4-2-222-2-2220001-11-1-222-223−23001-1−3−333000000000000000000000000000
χ3944-4-444-44-4-44-4-2-222-2-2220001-11-1-222-2−2323001-133−3−3000000000000000000000000000
χ4044-4-44-444-4-4-44-242-4-242-4000-22-2224-2-400002-20000000000000000000000000000000
χ4144-4-44-444-4-4-44-2-222-2-2220001-11-12-2-220023−23-11−33−33000000000000000000000000000
χ4244-4-44-444-4-4-44-2-222-2-2220001-11-12-2-2200−2323-113−33−3000000000000000000000000000
χ434-44-4400-44-40044-4-4-4-4440004-4-4400000000000000000000000000000000000000000
χ444-44-4400-44-4004-2-42-424-2000-222-20000000000000000000000000000i6−i6i6−i6000000000
χ454-44-4400-44-4004-2-42-424-2000-222-20000000000000000000000000000−i6i6−i6i6000000000
χ464-44-4400-44-400-242-42-4-24000-222-2000000000000000000000000i6−i6i6−i60000000000000
χ474-44-4400-44-400-242-42-4-24000-222-2000000000000000000000000−i6i6−i6i60000000000000
χ484-4-44400-4-44004444-4-4-4-400044-4-400000000000000000000000000000000000000000
χ494-4-44400-4-44004-24-2-42-42000-2-22200000000000000000000000000006−6−66000000000
χ504-4-44400-4-44004-24-2-42-42000-2-2220000000000000000000000000000−666−6000000000
χ514-4-44400-4-4400-24-242-42-4000-2-2220000000000000000000000006−6−660000000000000
χ524-4-44400-4-4400-24-242-42-4000-2-222000000000000000000000000−666−60000000000000
χ536666-366-3-3-3-3-3000000006-3-3000000000000000000220000-1-1-1-1000000000020000-1-1
χ546666-366-3-3-3-3-3000000006-3-3000000000000000000-2-2000011110000000000-2000011
χ556666-366-3-3-3-3-300000000-633000000000000000000220000-1-1-1-10000000000-2000011
χ566666-366-3-3-3-3-300000000-633000000000000000000-2-200001111000000000020000-1-1
χ576666-3-6-6-3-3-333000000000−3i33i30000000000000000002-20000-1-111000000000000000−i3i3
χ586666-3-6-6-3-3-333000000000−3i33i3000000000000000000-22000011-1-1000000000000000i3−i3
χ596666-3-6-6-3-3-3330000000003i3−3i30000000000000000002-20000-1-111000000000000000i3−i3
χ606666-3-6-6-3-3-3330000000003i3−3i3000000000000000000-22000011-1-1000000000000000−i3i3
χ618-88-8800-88-800-4-44444-4-40002-2-2200000000000000000000000000000000000000000
χ628-8-88800-8-8800-4-4-4-4444400022-2-200000000000000000000000000000000000000000
χ631212-12-12-612-12-666-6600000000000000000000000000000000000000000000000000000000
χ641212-12-12-6-1212-6666-600000000000000000000000000000000000000000000000000000000
χ6512-1212-12-6006-6600000000000000000000000000000000000000023−2300000000000000000
χ6612-1212-12-6006-66000000000000000000000000000000000000000−232300000000000000000
χ6712-12-1212-60066-6000000000000000000000000000000000000023−230000000000000000000
χ6812-12-1212-60066-60000000000000000000000000000000000000−23230000000000000000000

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