Finite Group Databasebeta

← Group #11722994

Character table — Group #11722994

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222224444444444448888121212121212121212121212121212121212121212121212121212181818181818363636363636108
order12223336666666663336666666663666244666666661212121212121212121212121212121222444466121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1
χ3111111111111111111111111111111111-1111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ511111111111111111111111111111111-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1
χ611111111111111111111111111111111-11-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11
χ711111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11
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
χ9222222-122-1-122-1222-1-122-1-1-1-1-12-1-1-1-1-120222-1-1-1-1-1-10000-1-1220000-1-1-1-1220000-1-100000
χ10222222-122-1-122-1222-1-122-1-1-1-1-12-1-1-1-1-120-222-1-1-1-1-1-1000011-2-200001111-2-200001100000
χ11222222-122-1-122-1222-1-122-1-1-1-1-12-1-1-1-1-1-202-2-21111110000-1-1220000-1-1-1-1-2-200001100000
χ12222222-122-1-122-1222-1-122-1-1-1-1-12-1-1-1-1-1-20-2-2-2111111000011-2-200001111220000-1-100000
χ1322222-122-1222-12-12-12-1-1-122-1-1-1-12-1-1-1-1220-1-122-1-1-1-122-1-10000-1-1-1-1000000220000-1-1000
χ1422222-122-1222-12-12-12-1-1-122-1-1-1-12-1-1-1-12-20-1-122-1-1-1-1-2-21100001111000000-2-2000011000
χ1522222-122-1222-12-12-12-1-1-122-1-1-1-12-1-1-1-1-22011-2-2111122-1-10000-1-1-1-1000000-2-2000011000
χ1622222-122-1222-12-12-12-1-1-122-1-1-1-12-1-1-1-1-2-2011-2-21111-2-21100001111000000220000-1-1000
χ172222-122-1222-1222-1-1-12-1-1-1-1222-1-1-1-1-1-102200000000-1-12222-1-1-1-1-1-1-1-1-1-10000220000-1-10
χ182222-122-1222-1222-1-1-12-1-1-1-1222-1-1-1-1-1-102-200000000-1-122-2-211-1-1-1-111110000-2-20000110
χ192222-122-1222-1222-1-1-12-1-1-1-1222-1-1-1-1-1-10-220000000011-2-222-1-11111-1-1-1-10000-2-20000110
χ202222-122-1222-1222-1-1-12-1-1-1-1222-1-1-1-1-1-10-2-20000000011-2-2-2-211111111110000220000-1-10
χ2122-2-2222-2-22-222-2-2-2222-2-22-22-2-22-222-2-200000000000000000000000000000002i−2i00002i−2i0
χ2222-2-2222-2-22-222-2-2-2222-2-22-22-2-22-222-2-20000000000000000000000000000000−2i2i0000−2i2i0
χ2322-2-2-1221-22-2-12-2-21-1-1211-112-2-2-11-1-11100000000000−i3i300003−3−i3−i3i3i333−3−300002i−2i0000−ii0
χ2422-2-2-1221-22-2-12-2-21-1-1211-112-2-2-11-1-11100000000000−i3i30000−33−i3−i3i3i3−3−3330000−2i2i0000i−i0
χ2522-2-2-1221-22-2-12-2-21-1-1211-112-2-2-11-1-11100000000000i3−i300003−3i3i3−i3−i333−3−30000−2i2i0000i−i0
χ2622-2-2-1221-22-2-12-2-21-1-1211-112-2-2-11-1-11100000000000i3−i30000−33i3i3−i3−i3−3−33300002i−2i0000−ii0
χ272-22-2222-2-2-2-2-2-22222222-2-2-2-22-2-222-22-20000000000000000000000000002-200002-200000
χ282-22-2222-2-2-2-2-2-22222222-2-2-2-22-2-222-22-2000000000000000000000000000-220000-2200000
χ292-22-222-1-2-211-2-2-1222-1-12-2111-11-2-1-11-1100000−i3i3−i3−i3i3i30000−i3i3000000−i3i3−i3i32-20000-1100000
χ302-22-222-1-2-211-2-2-1222-1-12-2111-11-2-1-11-1100000−i3i3−i3−i3i3i30000i3−i3000000i3−i3i3−i3-2200001-100000
χ312-22-222-1-2-211-2-2-1222-1-12-2111-11-2-1-11-1100000i3−i3i3i3−i3−i30000−i3i3000000−i3i3−i3i3-2200001-100000
χ322-22-222-1-2-211-2-2-1222-1-12-2111-11-2-1-11-1100000i3−i3i3i3−i3−i30000i3−i3000000i3−i3i3−i32-20000-1100000
χ332-2-2222222-22-2-2-2-2-2222-22-22-2-22-2-22-2-22000000000000000000000000000002i−2i00002i−2i000
χ342-2-2222222-22-2-2-2-2-2222-22-22-2-22-2-22-2-2200000000000000000000000000000−2i2i0000−2i2i000
χ352-2-222-122-1-22-21-21-2-12-11-1-2211-11-2-111-1000−i3i300−i3i3−i3i3003−300003−33−30000002i−2i0000−ii000
χ362-2-222-122-1-22-21-21-2-12-11-1-2211-11-2-111-1000−i3i300−i3i3−i3i300−330000−33−33000000−2i2i0000i−i000
χ372-2-222-122-1-22-21-21-2-12-11-1-2211-11-2-111-1000i3−i300i3−i3i3−i3003−300003−33−3000000−2i2i0000i−i000
χ382-2-222-122-1-22-21-21-2-12-11-1-2211-11-2-111-1000i3−i300i3−i3i3−i300−330000−33−330000002i−2i0000−ii000
χ3944444-2-24-2-2-24-2-2-24-2-21-2-2-2-2111-2-21111400-2-2-2-2111100000000000000000000000000000
χ4044444-2-24-2-2-24-2-2-24-2-21-2-2-2-2111-2-21111-4002222-1-1-1-100000000000000000000000000000
χ414444-24-2-24-2-2-24-24-2-21-2-2-211-2-2-2-211111004000000000000-2-2-2-2000011110000000000000
χ424444-24-2-24-2-2-24-24-2-21-2-2-211-2-2-2-21111100-400000000000022220000-1-1-1-10000000000000
χ434444-2-24-2-244-2-24-2-21-2-211-2-2-2-2-21-2111104000000000-2-2-2-20000111100000000000000000
χ444444-2-24-2-244-2-24-2-21-2-211-2-2-2-2-21-211110-400000000022220000-1-1-1-100000000000000000
χ4544-4-444-2-4-4-22442-4-44-2-2-4-4-22-22242-2-2220000000000000000000000000000000000000000
χ4644-4-44-24-424-44-2-42-4-24-2224-4-222-2-4-2-2220000000000000000000000000000000000000000
χ4744-4-44-2-2-42-224-222-4-2-2122-221-1-1-2211-1-100000003-3-3300000000000000000000000000000
χ4844-4-44-2-2-42-224-222-4-2-2122-221-1-1-2211-1-10000000-333-300000000000000000000000000000
χ4944-4-4-24-22-4-22-242-42-21-2221-1-222-2-111-1-10000000000000000023−230000−3−3330000000000000
χ5044-4-4-24-22-4-22-242-42-21-2221-1-222-2-111-1-100000000000000000−2323000033−3−30000000000000
χ5144-4-4-2-24224-4-2-2-4221-2-2-1-1-22-2221211-1-100000000000−2i32i3000000i3i3−i3−i300000000000000000
χ5244-4-4-2-24224-4-2-2-4221-2-2-1-1-22-2221211-1-1000000000002i3−2i3000000−i3−i3i3i300000000000000000
χ534-44-44-24-42-4-4-424-24-24-2-22-4-42-2224-22-220000000000000000000000000000000000000000
χ544-44-44-2-2-4222-42-2-24-2-21-2222-11-12-21-11-100000−2i32i3i3i3−i3−i300000000000000000000000000000
χ554-44-44-2-2-4222-42-2-24-2-21-2222-11-12-21-11-1000002i3−2i3−i3−i3i3i300000000000000000000000000000
χ564-44-4-2442-4-4-42-444-2-2-24-2222-44-42-2-22-220000000000000000000000000000000000000000
χ574-44-4-24-22-4222-4-24-2-21-2-22-1-12-22211-11-1000000000000000−2i32i3000000i3−i3i3−i30000000000000
χ584-44-4-24-22-4222-4-24-2-21-2-22-1-12-22211-11-10000000000000002i3−2i3000000−i3i3−i3i30000000000000
χ594-44-4-2-2422-4-4224-2-21-2-21-1222-22-1-21-11-100000000000000000003i−3i−3i3i00000000000000000
χ604-44-4-2-2422-4-4224-2-21-2-21-1222-22-1-21-11-10000000000000000000−3i3i3i−3i00000000000000000
χ614-4-4444-2442-2-4-42-4-44-2-2-442-222-2-42-222-20000000000000000000000000000000000000000
χ624-4-444-2-24-22-2-4222-4-2-212-22-2-1-11221-1-11000−2i32i300i3−i3i3−i300000000000000000000000000000
χ634-4-444-2-24-22-2-4222-4-2-212-22-2-1-11221-1-110002i3−2i300−i3i3−i3i300000000000000000000000000000
χ644-4-44-244-24-442-4-4-42-2-242-22-2-4-4422-222-20000000000000000000000000000000000000000
χ654-4-44-24-2-242-22-42-42-21-22-2-1122-22-11-1-11000000000000000000000003i−3i−3i3i0000000000000
χ664-4-44-24-2-242-22-42-42-21-22-2-1122-22-11-1-1100000000000000000000000−3i3i3i−3i0000000000000
χ674-4-44-2-24-2-2-4422-4221-2-2-112-222-2-121-1-11000000000000023−230000−33−3300000000000000000
χ684-4-44-2-24-2-2-4422-4221-2-2-112-222-2-121-1-110000000000000−232300003−33−300000000000000000
χ698888-4-4-4-4-4-4-4-4-4-4-4-4222222222222-1-1-1-10000000000000000000000000000000000000000
χ7088-8-8-4-4-444-44-4-4444222-2-22-22-2-22-2-1-1110000000000000000000000000000000000000000
χ718-88-8-4-4-4444444-4-4-42222-2-2-2-22-2-22-11-110000000000000000000000000000000000000000
χ728-8-88-4-4-4-4-44-444444222-22-22-2-22-2-2-111-10000000000000000000000000000000000000000

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