Finite Group Databasebeta

← Group #11722979

Character table — Group #11722979

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222224444444444448888121212121212121212121212121212121212121212121212121212181818181818363636363636108
order1222333666666666333666666666366644412121212121212121212121212121212121212121212121222444466121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1
χ3111111111111111111111111111111111-11111111-1-111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11
χ511111111111111111111111111111111-111-1-1111111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1
χ611111111111111111111111111111111-11-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11
χ711111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ9222222-1222-12-1-1222-1-122-1-1-1-12-1-1-1-1-1-1202-1-122-1-1002200-1-1-1-10000-1-1-1-1220000-1-100000
χ10222222-1222-12-1-1222-1-122-1-1-1-12-1-1-1-1-1-120-2-1-1-2-211002200-1-1-1-100001111-2-200001100000
χ11222222-1222-12-1-1222-1-122-1-1-1-12-1-1-1-1-1-1-2021122-1-100-2-20011110000-1-1-1-1-2-200001100000
χ12222222-1222-12-1-1222-1-122-1-1-1-12-1-1-1-1-1-1-20-211-2-21100-2-200111100001111220000-1-100000
χ1322222-1222-12-122-12-12-1-1-122-1-1-12-1-1-1-1-102200-1-122-1-100220000-1-1-1-1-1-1-1-100002200-1-1000
χ1422222-1222-12-122-12-12-1-1-122-1-1-12-1-1-1-1-102-20011-2-2-1-100220000-1-1-1-111110000-2-20011000
χ1522222-1222-12-122-12-12-1-1-122-1-1-12-1-1-1-1-10-2200-1-1221100-2-200001111-1-1-1-10000-2-20011000
χ1622222-1222-12-122-12-12-1-1-122-1-1-12-1-1-1-1-10-2-20011-2-21100-2-200001111111100002200-1-1000
χ172222-122-1-1222222-1-1-12-1-1-1-122-1-12-1-1-1-122022000022-1-1-1-1-1-1-1-1-1-1-1-100000022000000-1-10
χ182222-122-1-1222222-1-1-12-1-1-1-122-1-12-1-1-1-12-20220000-2-2-1-111-1-1-1-11111000000-2-2000000110
χ192222-122-1-1222222-1-1-12-1-1-1-122-1-12-1-1-1-1-220-2-200002211-1-11111-1-1-1-1000000-2-2000000110
χ202222-122-1-1222222-1-1-12-1-1-1-122-1-12-1-1-1-1-2-20-2-20000-2-211111111111100000022000000-1-10
χ2122-2-22222-222-2-2-2-2-22222-22-22-2-2-2-222-2-20000000000000000000000000002-200002-200000
χ2222-2-22222-222-2-2-2-2-22222-22-22-2-2-2-222-2-2000000000000000000000000000-220000-2200000
χ2322-2-222-12-22-1-211-2-22-1-12-2-11-11-211-1-1110003−3003−300000033−3−3000033−3−32-20000-1100000
χ2422-2-222-12-22-1-211-2-22-1-12-2-11-11-211-1-1110003−300−3300000033−3−30000−3−333-2200001-100000
χ2522-2-222-12-22-1-211-2-22-1-12-2-11-11-211-1-111000−33003−3000000−3−333000033−3−3-2200001-100000
χ2622-2-222-12-22-1-211-2-22-1-12-2-11-11-211-1-111000−3300−33000000−3−3330000−3−3332-20000-1100000
χ272-22-2222-2-2-2-2-22-222222-2-2-2-2-2222-22-22-2000000000000000000000000000002-20000002-20
χ282-22-2222-2-2-2-2-22-222222-2-2-2-2-2222-22-22-200000000000000000000000000000-22000000-220
χ292-22-2-12211-2-2-22-22-1-1-121111-22-1-1-2-11-1100000000000−i3i3−i3i3−i3i3−i3i3−i3−i3i3i30000002-2000000-110
χ302-22-2-12211-2-2-22-22-1-1-121111-22-1-1-2-11-1100000000000−i3i3i3−i3−i3i3−i3i3i3i3−i3−i3000000-220000001-10
χ312-22-2-12211-2-2-22-22-1-1-121111-22-1-1-2-11-1100000000000i3−i3−i3i3i3−i3i3−i3−i3−i3i3i3000000-220000001-10
χ322-22-2-12211-2-2-22-22-1-1-121111-22-1-1-2-11-1100000000000i3−i3i3−i3i3−i3i3−i3i3i3−i3−i30000002-2000000-110
χ332-2-22222-22-2-22-22-2-2222-22-22-2-2-2-222-2-2200000000000000000000000000000002i−2i002i−2i000
χ342-2-22222-22-2-22-22-2-2222-22-22-2-2-2-222-2-220000000000000000000000000000000−2i2i00−2i2i000
χ352-2-222-12-221-2-1-221-2-12-11-1-22111-2-1-111-100000−i3i3003−3000000003−33−3−i3i3−i3i300002i−2i00−ii000
χ362-2-222-12-221-2-1-221-2-12-11-1-22111-2-1-111-100000−i3i300−3300000000−33−33−i3i3−i3i30000−2i2i00i−i000
χ372-2-222-12-221-2-1-221-2-12-11-1-22111-2-1-111-100000i3−i3003−3000000003−33−3i3−i3i3−i30000−2i2i00i−i000
χ382-2-222-12-221-2-1-221-2-12-11-1-22111-2-1-111-100000i3−i300−3300000000−33−33i3−i3i3−i300002i−2i00−ii000
χ3944444-2-244-2-2-2-2-2-24-2-21-2-2-2-211-2-21111100400-2-2-2-20000000000000011110000000000000
χ4044444-2-244-2-2-2-2-2-24-2-21-2-2-2-211-2-21111100-400222200000000000000-1-1-1-10000000000000
χ414444-24-2-2-24-24-2-24-2-21-2-2-211-2-2-21-21111400-2-2000000-2-2001111000000000000000000000
χ424444-24-2-2-24-24-2-24-2-21-2-2-211-2-2-21-21111-400220000002200-1-1-1-1000000000000000000000
χ434444-2-24-2-2-24-244-2-21-2-211-2-2-2-21-2-21111040000000-2-200-2-20000111100000000000000000
χ444444-2-24-2-2-24-244-2-21-2-211-2-2-2-21-2-211110-400000002200220000-1-1-1-100000000000000000
χ4544-4-44-244-4-242-4-42-4-24-2-224-4-222-42-2-2220000000000000000000000000000000000000000
χ4644-4-44-2-24-4-2-22222-4-2-21-22-221-122-111-1-1000000023−2300000000000000−3−3330000000000000
χ4744-4-44-2-24-4-2-22222-4-2-21-22-221-122-111-1-10000000−23230000000000000033−3−30000000000000
χ4844-4-4-244-2244-4-4-4-42-2-24-22-224-422-4-2-2220000000000000000000000000000000000000000
χ4944-4-4-24-2-224-2-422-42-21-2-221-1-222-1211-1-100023−230000000000−3−333000000000000000000000
χ5044-4-4-24-2-224-2-422-42-21-2-221-1-222-1211-1-1000−2323000000000033−3−3000000000000000000000
χ5144-4-4-2-24-22-242-4-4221-2-21-1-22-22-12211-1-100000000000000000003i−3i−3i3i00000000000000000
χ5244-4-4-2-24-22-242-4-4221-2-21-1-22-22-12211-1-10000000000000000000−3i3i3i−3i00000000000000000
χ534-44-444-2-4-4-42-4-22444-2-2-4-4222-24-22-22-220000000000000000000000000000000000000000
χ544-44-44-24-4-42-424-4-24-24-222-4-42-2-242-22-220000000000000000000000000000000000000000
χ554-44-44-2-2-4-4222-22-24-2-212222-11-2-2-11-11-1000000000000000000000003i−3i−3i3i0000000000000
χ564-44-44-2-2-4-4222-22-24-2-212222-11-2-2-11-11-100000000000000000000000−3i3i3i−3i0000000000000
χ574-44-4-24-222-42-4-224-2-21-222-1-12-2-2121-11-100000000000−2i32i300i3−i3i3−i3000000000000000000000
χ584-44-4-24-222-42-4-224-2-21-222-1-12-2-2121-11-1000000000002i3−2i300−i3i3−i3i3000000000000000000000
χ594-44-4-2-24222-424-4-2-21-2-2-1-1222-21-221-11-10000000000000−2i32i30000i3i3−i3−i300000000000000000
χ604-44-4-2-24222-424-4-2-21-2-2-1-1222-21-221-11-100000000000002i3−2i30000−i3−i3i3i300000000000000000
χ614-4-4444-2-44-4242-2-4-44-2-2-442-222-42-2-222-20000000000000000000000000000000000000000
χ624-4-444-2-2-4422-22-22-4-2-212-22-2-1-12211-1-1100000−2i32i30000000000000000i3−i3i3−i30000000000000
χ634-4-444-2-2-4422-22-22-4-2-212-22-2-1-12211-1-11000002i3−2i30000000000000000−i3i3−i3i30000000000000
χ644-4-44-2442-2-4-44-44-42-2-242-22-2-4-4224-222-20000000000000000000000000000000000000000
χ654-4-44-24-22-2-4242-2-42-21-22-2-11222-1-21-1-110000000000000003i−3i−3i3i000000000000000000000
χ664-4-44-24-22-2-4242-2-42-21-22-2-11222-1-21-1-11000000000000000−3i3i3i−3i000000000000000000000
χ674-4-44-2-242-22-4-2-44221-2-2-112-222-12-21-1-1100000000023−2300000000−33−3300000000000000000
χ684-4-44-2-242-22-4-2-44221-2-2-112-222-12-21-1-11000000000−2323000000003−33−300000000000000000
χ698888-4-4-4-4-4-4-4-4-4-4-4-4222222222222-1-1-1-10000000000000000000000000000000000000000
χ7088-8-8-4-4-4-44-4-4444442222-22-22-2-2-2-2-1-1110000000000000000000000000000000000000000
χ718-88-8-4-4-444444-44-4-4222-2-2-2-2-2222-2-11-110000000000000000000000000000000000000000
χ728-8-88-4-4-44-444-44-444222-22-22-2-2-2-22-111-10000000000000000000000000000000000000000

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