Finite Group Databasebeta

← Group #11722993

Character table — Group #11722993

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order12223336666666663336666666664444121212121212121236664121212121212121212121212121212121212121222666644121212122
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
χ9222222-122-1-122-1222-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1022220000-1-1-1-1-1-1-1-1000022-1-1-1-10000000
χ10222222-122-1-122-1222-1-122-1-1-1-12-1-122-2-2-1-1-1-11111-1-1-1-1022-2-20000-1-1-1-111110000-2-211110000000
χ11222222-122-1-122-1222-1-122-1-1-1-12-1-1-2-2221111-1-1-1-1-1-1-1-10-2-22200001111-1-1-1-10000-2-211110000000
χ12222222-122-1-122-1222-1-122-1-1-1-12-1-1-2-2-2-211111111-1-1-1-10-2-2-2-2000011111111000022-1-1-1-10000000
χ1322222-122-1222-122-1-12-1-1-122-1-1-12-1002200002222-1-1-1-1200-1-122-1-10000-1-1-1-1-1-1-1-10000000200-1-10
χ1422222-122-1222-122-1-12-1-1-122-1-1-12-1002200002222-1-1-1-1-200-1-1-2-2110000-1-1-1-111110000000-200110
χ1522222-122-1222-122-1-12-1-1-122-1-1-12-100-2-20000-2-2-2-2-1-1-1-12001122-1-100001111-1-1-1-10000000-200110
χ1622222-122-1222-122-1-12-1-1-122-1-1-12-100-2-20000-2-2-2-2-1-1-1-1-20011-2-2110000111111110000000200-1-10
χ172222-122-1222-122-12-1-12-1-1-1-122-1-12220022220000-1-1-1-12-1-100-1-122-1-1-1-10000-1-1-1-100000020-1-1000
χ182222-122-1222-122-12-1-12-1-1-1-122-1-12220022220000-1-1-1-1-2-1-10011-2-2-1-1-1-100001111000000-2011000
χ192222-122-1222-122-12-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-121100-1-12211110000-1-1-1-1000000-2011000
χ202222-122-1222-122-12-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-1-2110011-2-211110000111100000020-1-1000
χ2122-2-22222-22-2-2-2-2-222222-22-22-2-2-2-2002i−2i00002i2i−2i−2i22-2-20002i−2i000000002i2i−2i−2i00000000000000000
χ2222-2-22222-22-2-2-2-2-222222-22-22-2-2-2-200−2i2i0000−2i−2i2i2i22-2-2000−2i2i00000000−2i−2i2i2i00000000000000000
χ2322-2-222-12-2-11-2-21-222-1-12-2-11-11-211002i−2i33−3−3−i−iii-1-1110002i−2i000033−3−3−i−iii000000−i3−i3i3i30000000
χ2422-2-222-12-2-11-2-21-222-1-12-2-11-11-211002i−2i−3−333−i−iii-1-1110002i−2i0000−3−333−i−iii000000i3i3−i3−i30000000
χ2522-2-222-12-2-11-2-21-222-1-12-2-11-11-21100−2i2i33−3−3ii−i−i-1-111000−2i2i000033−3−3ii−i−i000000i3i3−i3−i30000000
χ2622-2-222-12-2-11-2-21-222-1-12-2-11-11-21100−2i2i−3−333ii−i−i-1-111000−2i2i0000−3−333ii−i−i000000−i3−i3i3i30000000
χ2722-2-22-12212-2-21-2-2-1-12-1-112-2-111-21002i−2i00002i2i−2i−2i-1-111000−ii003−30000−i−iii33−3−30000000000−i3i30
χ2822-2-22-12212-2-21-2-2-1-12-1-112-2-111-21002i−2i00002i2i−2i−2i-1-111000−ii00−330000−i−iii−3−3330000000000i3−i30
χ2922-2-22-12212-2-21-2-2-1-12-1-112-2-111-2100−2i2i0000−2i−2i2i2i-1-111000i−i003−30000ii−i−i33−3−30000000000i3−i30
χ3022-2-22-12212-2-21-2-2-1-12-1-112-2-111-2100−2i2i0000−2i−2i2i2i-1-111000i−i00−330000ii−i−i−3−3330000000000−i3i30
χ312-22-2222-22-22-2-2-22-2222-22-22-22-2-2-22i−2i002i−2i2i−2i00002-22-202i−2i0000002i−2i2i−2i000000000000000000000
χ322-22-2222-22-22-2-2-22-2222-22-22-22-2-2-2−2i2i00−2i2i−2i2i00002-22-20−2i2i000000−2i2i−2i2i000000000000000000000
χ332-22-222-1-221-1-2-212-22-1-1-221-11-1-2112i−2i00−ii−ii3−33−3-11-1102i−2i000000−ii−ii3−33−3000000−i3i3−i3i30000000
χ342-22-222-1-221-1-2-212-22-1-1-221-11-1-2112i−2i00−ii−ii−33−33-11-1102i−2i000000−ii−ii−33−33000000i3−i3i3−i30000000
χ352-22-222-1-221-1-2-212-22-1-1-221-11-1-211−2i2i00i−ii−i3−33−3-11-110−2i2i000000i−ii−i3−33−3000000i3−i3i3−i30000000
χ362-22-222-1-221-1-2-212-22-1-1-221-11-1-211−2i2i00i−ii−i−33−33-11-110−2i2i000000i−ii−i−33−33000000−i3i3−i3i30000000
χ372-22-2-12212-221-2-2-1-2-1-121-11-1-2211-22i−2i002i−2i2i−2i0000-11-110−ii003−300−ii−ii00003−33−300000000−i3i3000
χ382-22-2-12212-221-2-2-1-2-1-121-11-1-2211-22i−2i002i−2i2i−2i0000-11-110−ii00−3300−ii−ii0000−33−3300000000i3−i3000
χ392-22-2-12212-221-2-2-1-2-1-121-11-1-2211-2−2i2i00−2i2i−2i2i0000-11-110i−i003−300i−ii−i00003−33−300000000i3−i3000
χ402-22-2-12212-221-2-2-1-2-1-121-11-1-2211-2−2i2i00−2i2i−2i2i0000-11-110i−i00−3300i−ii−i0000−33−3300000000−i3i3000
χ412-2-22222-2-2-2-2222-2-2222-2-2-2-2-2-22220000000000002-2-220000000000000000000002-22-2-220000000
χ422-2-22222-2-2-2-2222-2-2222-2-2-2-2-2-22220000000000002-2-22000000000000000000000-22-222-20000000
χ432-2-2222-1-2-21122-1-2-22-1-1-2-211112-1-10000−i3i3i3−i3−i3i3i3−i3-111-1000000000−i3i3i3−i3−i3i3i3−i300002-2-111-10000000
χ442-2-2222-1-2-21122-1-2-22-1-1-2-211112-1-10000−i3i3i3−i3i3−i3−i3i3-111-1000000000−i3i3i3−i3i3−i3−i3i30000-221-1-110000000
χ452-2-2222-1-2-21122-1-2-22-1-1-2-211112-1-10000i3−i3−i3i3−i3i3i3−i3-111-1000000000i3−i3−i3i3−i3i3i3−i30000-221-1-110000000
χ462-2-2222-1-2-21122-1-2-22-1-1-2-211112-1-10000i3−i3−i3i3i3−i3−i3i3-111-1000000000i3−i3−i3i3i3−i3−i3i300002-2-111-10000000
χ4744444-2-24-2-2-24-2-24-2-2-21-2-2-2-211-2-2100440000-2-2-2-21111000-2-200000000111100000000000000000
χ4844444-2-24-2-2-24-2-24-2-2-21-2-2-2-211-2-2100-4-40000222211110002200000000-1-1-1-100000000000000000
χ494444-24-2-24-2-2-24-2-24-21-2-2-211-2-2-21-24400-2-2-2-2000011110-2-20000001111000000000000000000000
χ504444-24-2-24-2-2-24-2-24-21-2-2-211-2-2-21-2-4-400222200001111022000000-1-1-1-1000000000000000000000
χ514444-2-24-2-244-2-24-2-21-2-211-2-2-2-21-2-2000000000000111140000-2-2-2-20000000011110000000000000
χ524444-2-24-2-244-2-24-2-21-2-211-2-2-2-21-2-20000000000001111-40000222200000000-1-1-1-10000000000000
χ5344-4-44-2-242-22-422-4-2-2-21-22-221-122-1004i−4i0000−2i−2i2i2i11-1-1000−2i2i00000000ii−i−i00000000000000000
χ5444-4-44-2-242-22-422-4-2-2-21-22-221-122-100−4i4i00002i2i−2i−2i11-1-10002i−2i00000000−i−iii00000000000000000
χ5544-4-4-244-2-44-42-4-424-2-24-22-224-422-4000000000000-2-2220000000000000000000000000000000000
χ5644-4-4-24-2-2-4-222-4224-21-2-221-1-222-1200002323−23−23000011-1-1000000000−3−333000000000000000000000
χ5744-4-4-24-2-2-4-222-4224-21-2-221-1-222-120000−23−232323000011-1-100000000033−3−3000000000000000000000
χ5844-4-4-2-24-224-422-42-21-2-21-1-22-22-12200000000000011-1-1000000023−2300000000−3−3330000000000000
χ5944-4-4-2-24-224-422-42-21-2-21-1-22-22-12200000000000011-1-10000000−23230000000033−3−30000000000000
χ604-44-44-24-4-2-44-42-442-24-22-2-442-22-42000000000000-22-220000000000000000000000000000000000
χ614-44-44-2-2-4-22-2-42242-2-212-22-2-1122-10000000023−2323−231-11-10000000000000−33−3300000000000000000
χ624-44-44-2-2-4-22-2-42242-2-212-22-2-1122-100000000−2323−23231-11-100000000000003−33−300000000000000000
χ634-44-4-24-2242-22-42-2-4-21-22-2-112-22-124i−4i00−2i2i−2i2i00001-11-10−2i2i000000i−ii−i000000000000000000000
χ644-44-4-24-2242-22-42-2-4-21-22-2-112-22-12−4i4i002i−2i2i−2i00001-11-102i−2i000000−ii−ii000000000000000000000
χ654-44-4-2-242-2-4422-4-221-2-2-112-22-2-1220000000000001-11-10000023−230000000000−33−330000000000000
χ664-44-4-2-242-2-4422-4-221-2-2-112-22-2-1220000000000001-11-100000−232300000000003−33−30000000000000
χ674-4-444-24-42-4-44-24-42-24-222-4-422-24-2000000000000-222-20000000000000000000000000000000000
χ684-4-444-2-2-42224-2-2-42-2-212222-1-1-2-2100000000−2i32i32i3−2i31-1-110000000000000i3−i3−i3i300000000000000000
χ694-4-444-2-2-42224-2-2-42-2-212222-1-1-2-21000000002i3−2i3−2i32i31-1-110000000000000−i3i3i3−i300000000000000000
χ704-4-44-2442-4-4-4-2442-4-2-242222-4-4-2-24000000000000-222-20000000000000000000000000000000000
χ714-4-44-24-22-422-24-22-4-21-222-1-122-21-20000−2i32i32i3−2i300001-1-11000000000i3−i3−i3i3000000000000000000000
χ724-4-44-24-22-422-24-22-4-21-222-1-122-21-200002i3−2i3−2i32i300001-1-11000000000−i3i3i3−i3000000000000000000000
χ734-4-44-2-2422-4-4-2-24221-2-2-1-122221-2-20000000000001-1-11000000000000000003-3-330000000000000
χ744-4-44-2-2422-4-4-2-24221-2-2-1-122221-2-20000000000001-1-1100000000000000000-333-30000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-4-44-444444-42222-22-22-2-2-2-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-44-44-4444-44222-22-22-22-2-2-2000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-44444-4-4-444222-2-2-2-2-2-2222000000000000-111-10000000000000000000000000000000000

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