Finite Group Databasebeta

← Group #11723010

Character table — Group #11723010

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order12223336666666663336666666664444121212121212121236664121212121212121212121212121212121212121244121212122266664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-11111111-1-111111111-1-1-1-11111-1-1-1-1-1-11-111-1-1-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111-1-111-1-1-1-1111111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-11-1-111-1
χ61111111111111111111111111111-1-111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ9222222-12-12222-1-122-1-122-1-1-1-12-1-1002200002222-1-1-1-1200-1-122-1-10000-1-1-1-1-1-1-1-10000000200-1-10
χ10222222-12-12222-1-122-1-122-1-1-1-12-1-1002200002222-1-1-1-1-200-1-1-2-2110000-1-1-1-111110000000-200110
χ11222222-12-12222-1-122-1-122-1-1-1-12-1-100-2-20000-2-2-2-2-1-1-1-12001122-1-100001111-1-1-1-10000000-200110
χ12222222-12-12222-1-122-1-122-1-1-1-12-1-100-2-20000-2-2-2-2-1-1-1-1-20011-2-2110000111111110000000200-1-10
χ1322222-12-1222-1-1222-12-1-1-122-1-1-12-1220022220000-1-1-1-12-1-100-1-122-1-1-1-10000-1-1-1-100000020-1-1000
χ1422222-12-1222-1-1222-12-1-1-122-1-1-12-1220022220000-1-1-1-1-2-1-10011-2-2-1-1-1-100001111000000-2011000
χ1522222-12-1222-1-1222-12-1-1-122-1-1-12-1-2-200-2-2-2-20000-1-1-1-121100-1-12211110000-1-1-1-1000000-2011000
χ1622222-12-1222-1-1222-12-1-1-122-1-1-12-1-2-200-2-2-2-20000-1-1-1-1-2110011-2-211110000111100000020-1-1000
χ172222-12222-1-12222-1-1-12-1-1-1-122-1-122222-1-1-1-1-1-1-1-1-1-1-1-1022220000-1-1-1-1-1-1-1-1000022-1-1-1-10000000
χ182222-12222-1-12222-1-1-12-1-1-1-122-1-1222-2-2-1-1-1-11111-1-1-1-1022-2-20000-1-1-1-111110000-2-211110000000
χ192222-12222-1-12222-1-1-12-1-1-1-122-1-12-2-2221111-1-1-1-1-1-1-1-10-2-22200001111-1-1-1-10000-2-211110000000
χ202222-12222-1-12222-1-1-12-1-1-1-122-1-12-2-2-2-211111111-1-1-1-10-2-2-2-2000011111111000022-1-1-1-10000000
χ2122-2-22222-22-2-2-22-2-22222-2-2-22-2-22-22i−2i002i2i−2i−2i000022-2-202i−2i0000002i2i−2i−2i000000000000000000000
χ2222-2-22222-22-2-2-22-2-22222-2-2-22-2-22-2−2i2i00−2i−2i2i2i000022-2-20−2i2i000000−2i−2i2i2i000000000000000000000
χ2322-2-22-12-1-22-2112-2-2-12-1-11-2-2-111212i−2i002i2i−2i−2i0000-1-1110−ii003−300−i−iii000033−3−300000000−i3i3000
χ2422-2-22-12-1-22-2112-2-2-12-1-11-2-2-111212i−2i002i2i−2i−2i0000-1-1110−ii00−3300−i−iii0000−3−33300000000i3−i3000
χ2522-2-22-12-1-22-2112-2-2-12-1-11-2-2-11121−2i2i00−2i−2i2i2i0000-1-1110i−i003−300ii−i−i000033−3−300000000i3−i3000
χ2622-2-22-12-1-22-2112-2-2-12-1-11-2-2-11121−2i2i00−2i−2i2i2i0000-1-1110i−i00−3300ii−i−i0000−3−33300000000−i3i3000
χ2722-2-2-1222-2-11-2-22-21-1-12-11112-21-1-22i−2i00−i−iii−i3−i3i3i3-1-11102i−2i000000−i−iii−i3−i3i3i300000033−3−30000000
χ2822-2-2-1222-2-11-2-22-21-1-12-11112-21-1-22i−2i00−i−iiii3i3−i3−i3-1-11102i−2i000000−i−iiii3i3−i3−i3000000−3−3330000000
χ2922-2-2-1222-2-11-2-22-21-1-12-11112-21-1-2−2i2i00ii−i−i−i3−i3i3i3-1-1110−2i2i000000ii−i−i−i3−i3i3i3000000−3−3330000000
χ3022-2-2-1222-2-11-2-22-21-1-12-11112-21-1-2−2i2i00ii−i−ii3i3−i3−i3-1-1110−2i2i000000ii−i−ii3i3−i3−i300000033−3−30000000
χ312-22-2222-22-222-2-2-2-2222-2-22-2-222-2-2002i−2i00002i−2i2i−2i2-22-20002i−2i000000002i−2i2i−2i00000000000000000
χ322-22-2222-22-222-2-2-2-2222-2-22-2-222-2-200−2i2i0000−2i2i−2i2i2-22-2000−2i2i00000000−2i2i−2i2i00000000000000000
χ332-22-222-1-2-1-222-211-22-1-1-2-2-111-1211002i−2i00002i−2i2i−2i-11-11000−ii003−30000−ii−ii3−33−30000000000−i3i30
χ342-22-222-1-2-1-222-211-22-1-1-2-2-111-1211002i−2i00002i−2i2i−2i-11-11000−ii00−330000−ii−ii−33−330000000000i3−i30
χ352-22-222-1-2-1-222-211-22-1-1-2-2-111-121100−2i2i0000−2i2i−2i2i-11-11000i−i003−30000i−ii−i3−33−30000000000i3−i30
χ362-22-222-1-2-1-222-211-22-1-1-2-2-111-121100−2i2i0000−2i2i−2i2i-11-11000i−i00−330000i−ii−i−33−330000000000−i3i30
χ372-22-2-122-221-12-2-2-21-1-1211-11-22-11-2002i−2i−i3i3−i3i3−ii−ii-11-110002i−2i0000−i3i3−i3i3−ii−ii0000003−33−30000000
χ382-22-2-122-221-12-2-2-21-1-1211-11-22-11-2002i−2ii3−i3i3−i3−ii−ii-11-110002i−2i0000i3−i3i3−i3−ii−ii000000−33−330000000
χ392-22-2-122-221-12-2-2-21-1-1211-11-22-11-200−2i2i−i3i3−i3i3i−ii−i-11-11000−2i2i0000−i3i3−i3i3i−ii−i000000−33−330000000
χ402-22-2-122-221-12-2-2-21-1-1211-11-22-11-200−2i2ii3−i3i3−i3i−ii−i-11-11000−2i2i0000i3−i3i3−i3i−ii−i0000003−33−30000000
χ412-2-22222-2-2-2-2-22-222222-22-22-2-2-2-220000000000002-2-220000000000000000000002-22-2-220000000
χ422-2-22222-2-2-2-2-22-222222-22-22-2-2-2-220000000000002-2-22000000000000000000000-22-222-20000000
χ432-2-22-122-2-211-22-22-1-1-121-11-1-2-211200003−3−333−3−33-111-10000000003−3−333−3−330000-221-1-110000000
χ442-2-22-122-2-211-22-22-1-1-121-11-1-2-211200003−3−33−333−3-111-10000000003−3−33−333−300002-2-111-10000000
χ452-2-22-122-2-211-22-22-1-1-121-11-1-2-21120000−333−33−3−33-111-1000000000−333−33−3−3300002-2-111-10000000
χ462-2-22-122-2-211-22-22-1-1-121-11-1-2-21120000−333−3−333−3-111-1000000000−333−3−333−30000-221-1-110000000
χ4744444-2-2-2-244-2-2-2-24-2-21-2-2-2-211-2-21000000000000111140000-2-2-2-20000000011110000000000000
χ4844444-2-2-2-244-2-2-2-24-2-21-2-2-2-211-2-210000000000001111-40000222200000000-1-1-1-10000000000000
χ494444-24-24-2-2-244-2-2-2-21-2-2-211-2-2-21-200440000-2-2-2-21111000-2-200000000111100000000000000000
χ504444-24-24-2-2-244-2-2-2-21-2-2-211-2-2-21-200-4-40000222211110002200000000-1-1-1-100000000000000000
χ514444-2-24-24-2-2-2-244-21-2-211-2-2-2-21-2-24400-2-2-2-2000011110-2-20000001111000000000000000000000
χ524444-2-24-24-2-2-2-244-21-2-211-2-2-2-21-2-2-4-400222200001111022000000-1-1-1-1000000000000000000000
χ5344-4-444-2424-4-4-4-22-44-2-24-422-22-4-22000000000000-2-2220000000000000000000000000000000000
χ5444-4-44-2-2-224-422-22-4-2-21-22221-12-2-100000000000011-1-10000023−230000000000−3−3330000000000000
χ5544-4-44-2-2-224-422-22-4-2-21-22221-12-2-100000000000011-1-100000−2323000000000033−3−30000000000000
χ5644-4-4-24-242-22-4-4-222-21-2-22-1-1-2221200000000−2i3−2i32i32i311-1-10000000000000i3i3−i3−i300000000000000000
χ5744-4-4-24-242-22-4-4-222-21-2-22-1-1-22212000000002i32i3−2i3−2i311-1-10000000000000−i3−i3i3i300000000000000000
χ5844-4-4-2-24-2-4-22224-421-2-21-122-22-1-224i−4i00−2i−2i2i2i000011-1-10−2i2i000000ii−i−i000000000000000000000
χ5944-4-4-2-24-2-4-22224-421-2-21-122-22-1-22−4i4i002i2i−2i−2i000011-1-102i−2i000000−i−iii000000000000000000000
χ604-44-44-2424-44-22-4-4-4-24-2224-42-2-2-42000000000000-22-220000000000000000000000000000000000
χ614-44-44-2-22-2-44-2222-4-2-2122-22-11-22-10000000000001-11-1000000023−2300000000−33−330000000000000
χ624-44-44-2-22-2-44-2222-4-2-2122-22-11-22-10000000000001-11-10000000−2323000000003−33−30000000000000
χ634-44-4-24-2-4-22-24-4222-21-2221-12-2-2-12004i−4i0000−2i2i−2i2i1-11-1000−2i2i00000000i−ii−i00000000000000000
χ644-44-4-24-2-4-22-24-4222-21-2221-12-2-2-1200−4i4i00002i−2i2i−2i1-11-10002i−2i00000000−ii−ii00000000000000000
χ654-44-4-2-24242-2-22-4-421-2-2-1-1-222-21220000−2i32i3−2i32i300001-11-1000000000i3−i3i3−i3000000000000000000000
χ664-44-4-2-24242-2-22-4-421-2-2-1-1-222-212200002i3−2i32i3−2i300001-11-1000000000−i3i3−i3i3000000000000000000000
χ674-4-4444-2-42-4-4-442-244-2-2-442-222-42-2000000000000-222-20000000000000000000000000000000000
χ684-4-444-242-4-4-42-2-444-24-22-2-44222-4-2000000000000-222-20000000000000000000000000000000000
χ694-4-444-2-222-4-42-22-24-2-212-22-2-1-12210000000000001-1-11000000000000000003-3-330000000000000
χ704-4-444-2-222-4-42-22-24-2-212-22-2-1-12210000000000001-1-1100000000000000000-333-30000000000000
χ714-4-44-24-2-4222-442-2-2-21-22-2-11222-1-20000000023−23−23231-1-110000000000000−333−300000000000000000
χ724-4-44-24-2-4222-442-2-2-21-22-2-11222-1-200000000−232323−231-1-1100000000000003−3−3300000000000000000
χ734-4-44-2-242-4222-2-44-21-2-2-112-222-12-2000023−23−232300001-1-11000000000−333−3000000000000000000000
χ744-4-44-2-242-4222-2-44-21-2-2-112-222-12-20000−232323−2300001-1-110000000003−3−33000000000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-4-44-4444-4442222-2-2-22-2-22-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-44-44-4-44444222-2-22-2-222-2-2000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-444444-44-4-4222-22-22-2-2-2-22000000000000-111-10000000000000000000000000000000000

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