Finite Group Databasebeta

← Group #13137864

Character table — Group #13137864

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order12223446661212336666664121236661212121244121212121212121212124444488881212121224242424242424244121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-111-1-1
χ511111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1
χ92222222222222-12-12-1-12222-1-1-1-1-12-120022-1-1-1-1-1-1-1-100022002200000000-1-1-1-1000-1-100
χ102222222222222-12-12-1-12222-1-1-1-1-12-120022-1-1-1-1-1-1-1-1000-2-200-2-20000000011110001100
χ112222222222222-12-12-1-12-2-2-2-1-1-1-1-12-1200-2-211-1-111110002200-2-2000000001111000-1-100
χ122222222222222-12-12-1-12-2-2-2-1-1-1-1-12-1200-2-211-1-11111000-2-2002200000000-1-1-1-10001100
χ13222222222222-12-12-122-1222-1-1-1-12-12-100-1-122-1-1-1-1-1-12200022000000-1-1-1-1000000000-1-1
χ14222222222222-12-12-122-1222-1-1-1-12-12-100-1-122-1-1-1-1-1-1-2-2000-2-2000000111100000000011
χ15222222222222-12-12-122-1-2-2-2-1-1-1-12-12-10011-2-2-1-1111122000-2-20000001111000000000-1-1
χ16222222222222-12-12-122-1-2-2-2-1-1-1-12-12-10011-2-2-1-11111-2-200022000000-1-1-1-100000000011
χ1722222-2-2222-2-2222222220002222-2-2-2-2220000-2-2000000-2000000-2-222000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-20000-2-2000000200000022-2-2000000000000000
χ1922-2-222-22-2-22-222-22-2-2-220002-22-222-2-20000002-200002-20000000000000000000000002-2
χ2022-2-222-22-2-22-222-22-2-2-220002-22-222-2-20000002-20000-22000000000000000000000000-22
χ2122-2-222-22-2-22-2-12121-2-2-1000-11-112-1-21003−300-1133−3−32-20000000000033−3−3000000000-11
χ2222-2-222-22-2-22-2-12121-2-2-1000-11-112-1-21003−300-1133−3−3-2200000000000−3−3330000000001-1
χ2322-2-222-22-2-22-2-12121-2-2-1000-11-112-1-2100−3300-11−3−3332-200000000000−3−333000000000-11
χ2422-2-222-22-2-22-2-12121-2-2-1000-11-112-1-2100−3300-11−3−333-220000000000033−3−30000000001-1
χ2522-2-22-222-2-2-2222-22-2-2-220002-22-2-2-222000000-2200000002i−2i00000000000000000002i−2i00
χ2622-2-22-222-2-2-2222-22-2-2-220002-22-2-2-222000000-220000000−2i2i0000000000000000000−2i2i00
χ2722-2-22-222-2-2-222-1-2-1-2112000-11-111-2-1200003−31-13−33−30002i−2i000000000000−i3−i3i3i3000−ii00
χ2822-2-22-222-2-2-222-1-2-1-2112000-11-111-2-1200003−31-13−33−3000−2i2i000000000000i3i3−i3−i3000i−i00
χ2922-2-22-222-2-2-222-1-2-1-2112000-11-111-2-120000−331-1−33−330002i−2i000000000000i3i3−i3−i3000−ii00
χ3022-2-22-222-2-2-222-1-2-1-2112000-11-111-2-120000−331-1−33−33000−2i2i000000000000−i3−i3i3i3000i−i00
χ312-2-22200-2-220022-2-222-2-20002-2-2200002-2000000000000000−i2i2−i2i2002-2−i2i2−i2i2−i2i2−i2i20000000
χ322-2-22200-2-220022-2-222-2-20002-2-2200002-2000000000000000i2−i2i2−i2002-2i2−i2i2−i2i2−i2i2−i20000000
χ332-2-22200-2-220022-2-222-2-20002-2-220000-22000000000000000−i2i2i2−i200-22−i2i2−i2i2i2−i2i2−i20000000
χ342-2-22200-2-220022-2-222-2-20002-2-220000-22000000000000000i2−i2−i2i200-22i2−i2i2−i2−i2i2−i2i20000000
χ35444444444444-2-2-2-2-2-2-2-24441111-2-2-2-200-2-2-2-21111110000000000000000000000000000
χ36444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-200222211-1-1-1-10000000000000000000000000000
χ3744444-4-4444-4-44-24-24-2-24000-2-2-2-22-42-40000002200000000000000000000000000000000
χ3844444-4-4444-4-4-24-24-244-2000-2-2-2-2-42-420000002200000000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-200011112222000000-1-13-3-330000000000000000000000000000
χ4044444-4-4444-4-4-2-2-2-2-2-2-2-200011112222000000-1-1-333-30000000000000000000000000000
χ4144-4-444-44-4-44-44-2-4-2-4224000-22-22-242-4000000-2200000000000000000000000000000000
χ4244-4-444-44-4-44-4-2-22-2222-20001-11-1-2-2220023−23001-1−3−3330000000000000000000000000000
χ4344-4-444-44-4-44-4-2-22-2222-20001-11-1-2-22200−2323001-133−3−30000000000000000000000000000
χ4444-4-44-444-4-4-44-24242-4-4-2000-22-22-424-20000002-200000000000000000000000000000000
χ4544-4-44-444-4-4-44-2-22-2222-20001-11-122-2-2000023−23-11−33−330000000000000000000000000000
χ4644-4-44-444-4-4-44-2-22-2222-20001-11-122-2-20000−2323-113−33−30000000000000000000000000000
χ474-44-4400-44-400444-4-4-44-400044-4-400000000000000000000000000000000000000000000
χ484-44-4400-44-4004-242-42-2-4000-2-2220000000000000000000000000000000006−6−660000000
χ494-44-4400-44-4004-242-42-2-4000-2-222000000000000000000000000000000000−666−60000000
χ504-44-4400-44-400-24-2-42-442000-2-22200000000000000000000000000000i6−i6−i6i600000000000
χ514-44-4400-44-400-24-2-42-442000-2-22200000000000000000000000000000−i6i6i6−i600000000000
χ524-4-44400-4-44004-2-424-22-4000-222-200000000000000000000000−2i22i200000000i2−i2i2−i20000000
χ534-4-44400-4-44004-2-424-22-4000-222-2000000000000000000000002i2−2i200000000−i2i2−i2i20000000
χ544-4-44400-4-4400-242-4-24-42000-222-2000000000000000000000−2i22i2000000i2−i2i2−i200000000000
χ554-4-44400-4-4400-242-4-24-42000-222-20000000000000000000002i2−2i2000000−i2i2−i2i200000000000
χ566666-366-3-3-3-3-3000000006-3-300000000220000000000002000000-1-1-1-1000000002-1-10000
χ576666-366-3-3-3-3-3000000006-3-300000000-2-2000000000000-2000000111100000000-2110000
χ586666-366-3-3-3-3-300000000-63300000000220000000000002000000-1-1-1-100000000-2110000
χ596666-366-3-3-3-3-300000000-63300000000-2-2000000000000-20000001111000000002-1-10000
χ606666-3-6-6-3-3-333000000000−3i33i30000000022000000000000-200000011-1-1000000000−i3i30000
χ616666-3-6-6-3-3-333000000000−3i33i300000000-2-20000000000002000000-1-111000000000i3−i30000
χ626666-3-6-6-3-3-3330000000003i3−3i30000000022000000000000-200000011-1-1000000000i3−i30000
χ636666-3-6-6-3-3-3330000000003i3−3i300000000-2-20000000000002000000-1-111000000000−i3i30000
χ648-88-8800-88-800-4-4-4444-4400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-8-8800-4-444-4-4440002-2-2200000000000000000000000000000000000000000000
χ661212-12-12-612-12-666-6600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-6-1212-6666-600000000000000000000000000000000000000000000000000000000000
χ6812-1212-12-6006-66000000000000000000000000000000000000000000−2i32i300000000000000000
χ6912-1212-12-6006-660000000000000000000000000000000000000000002i3−2i300000000000000000
χ7012-12-1212-60066-60000000000000000000004-4000000000000000000000-22000000000000000
χ7112-12-1212-60066-6000000000000000000000-440000000000000000000002-2000000000000000

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