Finite Group Databasebeta

← Group #11723024

Character table — Group #11723024

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order1222333666666666333666666666444412121212121212123666412121212121212121212121212121212121212124412121212246612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ51111111111111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11-111-1-1-1
χ61111111111111111111111111111-1-111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
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
χ9222222-12-1222-1-1222-1-122-1-1-1-12-1-1002200002222-1-1-1-12-1-122-1-1000000-1-1-1-1-1-1-1-100000020-1-1000
χ10222222-12-1222-1-1222-1-122-1-1-1-12-1-1002200002222-1-1-1-1-2-1-1-2-211000000-1-1-1-11111000000-2011000
χ11222222-12-1222-1-1222-1-122-1-1-1-12-1-100-2-20000-2-2-2-2-1-1-1-121122-1-10000001111-1-1-1-1000000-2011000
χ12222222-12-1222-1-1222-1-122-1-1-1-12-1-100-2-20000-2-2-2-2-1-1-1-1-211-2-2110000001111111100000020-1-1000
χ1322222-12222-1-122-12-12-1-1-122-1-1-12-12222-1-1-1-1-1-1-1-1-1-1-1-1022000022-1-1-1-1-1-1-1-1000022-1-1-1-10000000
χ1422222-12222-1-122-12-12-1-1-122-1-1-12-122-2-2-1-1-1-11111-1-1-1-10-2-2000022-1-1-1-111110000-2-211110000000
χ1522222-12222-1-122-12-12-1-1-122-1-1-12-1-2-2221111-1-1-1-1-1-1-1-10220000-2-21111-1-1-1-10000-2-211110000000
χ1622222-12222-1-122-12-12-1-1-122-1-1-12-1-2-2-2-211111111-1-1-1-10-2-20000-2-211111111000022-1-1-1-10000000
χ172222-122-12-122222-1-1-12-1-1-1-122-1-12220022220000-1-1-1-1200-1-122-1-1-1-1-1-10000-1-1-1-10000000200-1-10
χ182222-122-12-122222-1-1-12-1-1-1-122-1-12220022220000-1-1-1-1-20011-2-2-1-1-1-1-1-1000011110000000-200110
χ192222-122-12-122222-1-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-1200-1-1221111110000-1-1-1-10000000-200110
χ202222-122-12-122222-1-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-1-20011-2-2111111000011110000000200-1-10
χ2122-2-2222-22-22-2-2-2-22222-2-22-22-22-2-2002i−2i00002i2i−2i−2i22-2-202i−2i00000000002i2i−2i−2i00000000000000000
χ2222-2-2222-22-22-2-2-2-22222-2-22-22-22-2-200−2i2i0000−2i−2i2i2i22-2-20−2i2i0000000000−2i−2i2i2i00000000000000000
χ2322-2-222-1-2-1-22-211-222-1-1-2-2-11-11211002i−2i00002i2i−2i−2i-1-1110−ii003−3000000−i−iii33−3−300000000−i3i3000
χ2422-2-222-1-2-1-22-211-222-1-1-2-2-11-11211002i−2i00002i2i−2i−2i-1-1110−ii00−33000000−i−iii−3−33300000000i3−i3000
χ2522-2-222-1-2-1-22-211-222-1-1-2-2-11-1121100−2i2i0000−2i−2i2i2i-1-1110i−i003−3000000ii−i−i33−3−300000000i3−i3000
χ2622-2-222-1-2-1-22-211-222-1-1-2-2-11-1121100−2i2i0000−2i−2i2i2i-1-1110i−i00−33000000ii−i−i−3−33300000000−i3i3000
χ2722-2-22-12-22-2-11-2-212-12-1112-2-11-1-21002i−2i−i3−i3i3i3−i−iii-1-11102i−2i000000−i3−i3i3i3−i−iii00000033−3−30000000
χ2822-2-22-12-22-2-11-2-212-12-1112-2-11-1-21002i−2ii3i3−i3−i3−i−iii-1-11102i−2i000000i3i3−i3−i3−i−iii000000−3−3330000000
χ2922-2-22-12-22-2-11-2-212-12-1112-2-11-1-2100−2i2i−i3−i3i3i3ii−i−i-1-1110−2i2i000000−i3−i3i3i3ii−i−i000000−3−3330000000
χ3022-2-22-12-22-2-11-2-212-12-1112-2-11-1-2100−2i2ii3i3−i3−i3ii−i−i-1-1110−2i2i000000i3i3−i3−i3ii−i−i00000033−3−30000000
χ312-22-2222-2-22-2-22-22-22222-2-2-2-22-22-22i−2i002i−2i2i−2i00002-22-200000002i−2i2i−2i2i−2i000000000000000000000
χ322-22-2222-2-22-2-22-22-22222-2-2-2-22-22-2−2i2i00−2i2i−2i2i00002-22-20000000−2i2i−2i2i−2i2i000000000000000000000
χ332-22-22-12-2-22112-2-1-2-12-1-11-2-21-11212i−2i00−ii−ii3−33−3-11-1100000002i−2i−ii−ii3−33−3000000−i3i3−i3i30000000
χ342-22-22-12-2-22112-2-1-2-12-1-11-2-21-11212i−2i00−ii−ii−33−33-11-1100000002i−2i−ii−ii−33−33000000i3−i3i3−i30000000
χ352-22-22-12-2-22112-2-1-2-12-1-11-2-21-1121−2i2i00i−ii−i3−33−3-11-110000000−2i2ii−ii−i3−33−3000000i3−i3i3−i30000000
χ362-22-22-12-2-22112-2-1-2-12-1-11-2-21-1121−2i2i00i−ii−i−33−33-11-110000000−2i2ii−ii−i−33−33000000−i3i3−i3i30000000
χ372-22-2-1221-2-1-2-22-221-1-12-1111-221-1-22i−2i002i−2i2i−2i0000-11-11000−i3i300−ii−ii−ii0000−i3i3−i3i300000000003−30
χ382-22-2-1221-2-1-2-22-221-1-12-1111-221-1-22i−2i002i−2i2i−2i0000-11-11000i3−i300−ii−ii−ii0000i3−i3i3−i30000000000−330
χ392-22-2-1221-2-1-2-22-221-1-12-1111-221-1-2−2i2i00−2i2i−2i2i0000-11-11000−i3i300i−ii−ii−i0000−i3i3−i3i30000000000−330
χ402-22-2-1221-2-1-2-22-221-1-12-1111-221-1-2−2i2i00−2i2i−2i2i0000-11-11000i3−i300i−ii−ii−i0000i3−i3i3−i300000000003−30
χ412-2-222222-2-2-22-22-2-2222-22-22-2-2-2-220000000000002-2-220000000000000000000002i−2i2i−2i−2i2i0000000
χ422-2-222222-2-2-22-22-2-2222-22-22-2-2-2-220000000000002-2-22000000000000000000000−2i2i−2i2i2i−2i0000000
χ432-2-222-122-2-21-1-221-2-12-11-1-22111-2-100003−3−33−i3i3i3−i3-111-10000000003−3−33−i3i3i3−i30000−2i2ii−i−ii0000000
χ442-2-222-122-2-21-1-221-2-12-11-1-22111-2-100003−3−33i3−i3−i3i3-111-10000000003−3−33i3−i3−i3i300002i−2i−iii−i0000000
χ452-2-222-122-2-21-1-221-2-12-11-1-22111-2-10000−333−3−i3i3i3−i3-111-1000000000−333−3−i3i3i3−i300002i−2i−iii−i0000000
χ462-2-222-122-2-21-1-221-2-12-11-1-22111-2-10000−333−3i3−i3−i3i3-111-1000000000−333−3i3−i3−i3i30000−2i2ii−i−ii0000000
χ4744444-2-24-24-2-2-2-2-24-2-21-2-2-2-211-2-2100440000-2-2-2-211110-2-20000000000111100000000000000000
χ4844444-2-24-24-2-2-2-2-24-2-21-2-2-2-211-2-2100-4-40000222211110220000000000-1-1-1-100000000000000000
χ494444-24-2-2-2-244-2-24-2-21-2-2-211-2-2-21-20000000000001111400-2-2-2-2000000000011110000000000000
χ504444-24-2-2-2-244-2-24-2-21-2-2-211-2-2-21-20000000000001111-40022220000000000-1-1-1-10000000000000
χ514444-2-24-24-2-2-244-2-21-2-211-2-2-2-21-2-24400-2-2-2-2000011110000000-2-21111000000000000000000000
χ524444-2-24-24-2-2-244-2-21-2-211-2-2-2-21-2-2-4-400222200001111000000022-1-1-1-1000000000000000000000
χ5344-4-44-2-2-4-2-4-222224-2-2122-221-1-22-1004i−4i0000−2i−2i2i2i11-1-10−2i2i0000000000ii−i−i00000000000000000
χ5444-4-44-2-2-4-2-4-222224-2-2122-221-1-22-100−4i4i00002i2i−2i−2i11-1-102i−2i0000000000−i−iii00000000000000000
χ5544-4-4-2442424-4-4-4-4-2-2-2422-224-4-22-4000000000000-2-2220000000000000000000000000000000000
χ5644-4-4-24-22-224-422-4-2-21-2221-1-22-2-1200000000000011-1-10000023−230000000000−3−3330000000000000
χ5744-4-4-24-22-224-422-4-2-21-2221-1-22-2-1200000000000011-1-100000−2323000000000033−3−30000000000000
χ5844-4-4-2-24242-22-4-42-21-2-2-1-1-22-221220000−2i3−2i32i32i3000011-1-1000000000i3i3−i3−i3000000000000000000000
χ5944-4-4-2-24242-22-4-42-21-2-2-1-1-22-2212200002i32i3−2i3−2i3000011-1-1000000000−i3−i3i3i3000000000000000000000
χ604-44-444-2-424-4-4-224-44-2-24-4222-2-4-22000000000000-22-220000000000000000000000000000000000
χ614-44-44-2-2-42422-22-2-4-2-21-2222-112-2-10000000023−2323−231-11-10000000000000−33−3300000000000000000
χ624-44-44-2-2-42422-22-2-4-2-21-2222-112-2-100000000−2323−23231-11-100000000000003−33−300000000000000000
χ634-44-4-24-222-2-4-4-2242-21-2-22-1-12-22120000000000001-11-1000−2i32i3000000000000i3−i3i3−i30000000000000
χ644-44-4-24-222-2-4-4-2242-21-2-22-1-12-22120000000000001-11-10002i3−2i3000000000000−i3i3−i3i30000000000000
χ654-44-4-2-242-4-2224-4-221-2-21-1222-2-1-224i−4i00−2i2i−2i2i00001-11-10000000−2i2ii−ii−i000000000000000000000
χ664-44-4-2-242-4-2224-4-221-2-21-1222-2-1-22−4i4i002i−2i2i−2i00001-11-100000002i−2i−ii−ii000000000000000000000
χ674-4-4444-242-4-442-2-4-44-2-2-442-222-42-2000000000000-222-20000000000000000000000000000000000
χ684-4-444-2-242-42-22-22-4-2-212-22-2-1-122100000000−2i32i32i3−2i31-1-110000000000000i3−i3−i3i300000000000000000
χ694-4-444-2-242-42-22-22-4-2-212-22-2-1-1221000000002i3−2i3−2i32i31-1-110000000000000−i3i3i3−i300000000000000000
χ704-4-44-244-2-42-44-44-42-2-242-22-2-4-4224000000000000-222-20000000000000000000000000000000000
χ714-4-44-24-2-222-442-2-42-21-22-2-11222-1-20000000000001-1-11000000000000000003i−3i−3i3i0000000000000
χ724-4-44-24-2-222-442-2-42-21-22-2-11222-1-20000000000001-1-1100000000000000000−3i3i3i−3i0000000000000
χ734-4-44-2-24-2-422-2-44221-2-2-112-222-12-2000023−23−232300001-1-11000000000−333−3000000000000000000000
χ744-4-44-2-24-2-422-2-44221-2-2-112-222-12-20000−232323−2300001-1-110000000003−3−33000000000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-44-44-44444-4222-2-22-22-22-2-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-444-444-44-442222-2-2-2-22-22-2000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-4-4444-44-444222-22-22-2-2-2-22000000000000-111-10000000000000000000000000000000000

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