Finite Group Databasebeta

← Group #11722995

Character table — Group #11722995

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order122233366666666633366666666644441212121212121212366641212121212121212121212121212121212121212226666246612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-11-111-1-1-1
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
χ61111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
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
χ9222222-1222-12-1-1222-1-122-1-1-1-12-1-1220022220000-1-1-1-12-1-122-1-100-1-1-1-10000-1-1-1-100000020-1-1000
χ10222222-1222-12-1-1222-1-122-1-1-1-12-1-1220022220000-1-1-1-1-2-1-1-2-21100-1-1-1-100001111000000-2011000
χ11222222-1222-12-1-1222-1-122-1-1-1-12-1-1-2-200-2-2-2-20000-1-1-1-121122-1-10011110000-1-1-1-1000000-2011000
χ12222222-1222-12-1-1222-1-122-1-1-1-12-1-1-2-200-2-2-2-20000-1-1-1-1-211-2-2110011110000111100000020-1-1000
χ1322222-122-1-12222-12-12-1-1-122-1-1-12-12222-1-1-1-1-1-1-1-1-1-1-1-1022000022-1-1-1-1-1-1-1-1000022-1-1-1-10000000
χ1422222-122-1-12222-12-12-1-1-122-1-1-12-122-2-2-1-1-1-11111-1-1-1-10220000-2-2-1-1-1-111110000-2-211110000000
χ1522222-122-1-12222-12-12-1-1-122-1-1-12-1-2-2221111-1-1-1-1-1-1-1-10-2-20000221111-1-1-1-10000-2-211110000000
χ1622222-122-1-12222-12-12-1-1-122-1-1-12-1-2-2-2-211111111-1-1-1-10-2-20000-2-211111111000022-1-1-1-10000000
χ172222-122-1222-1222-1-1-12-1-1-1-122-1-12002200002222-1-1-1-1200-1-122-1-10000-1-1-1-1-1-1-1-10000000200-1-10
χ182222-122-1222-1222-1-1-12-1-1-1-122-1-12002200002222-1-1-1-1-20011-2-2-1-10000-1-1-1-111110000000-200110
χ192222-122-1222-1222-1-1-12-1-1-1-122-1-1200-2-20000-2-2-2-2-1-1-1-1200-1-1221100001111-1-1-1-10000000-200110
χ202222-122-1222-1222-1-1-12-1-1-1-122-1-1200-2-20000-2-2-2-2-1-1-1-1-20011-2-2110000111111110000000200-1-10
χ2122-2-2222-22-2-222-2-2-22222-2-2-22-2-22-2002i−2i00002i2i−2i−2i22-2-200000002i−2i00002i2i−2i−2i00000000000000000
χ2222-2-2222-22-2-222-2-2-22222-2-2-22-2-22-200−2i2i0000−2i−2i2i2i22-2-20000000−2i2i0000−2i−2i2i2i00000000000000000
χ2322-2-22-12-2-11-222-21-2-12-1-11-2-2-11121002i−2i33−3−3−i−iii-1-11100000002i−2i33−3−3−i−iii000000−i3−i3i3i30000000
χ2422-2-22-12-2-11-222-21-2-12-1-11-2-2-11121002i−2i−3−333−i−iii-1-11100000002i−2i−3−333−i−iii000000i3i3−i3−i30000000
χ2522-2-22-12-2-11-222-21-2-12-1-11-2-2-1112100−2i2i33−3−3ii−i−i-1-1110000000−2i2i33−3−3ii−i−i000000i3i3−i3−i30000000
χ2622-2-22-12-2-11-222-21-2-12-1-11-2-2-1112100−2i2i−3−333ii−i−i-1-1110000000−2i2i−3−333ii−i−i000000−i3−i3i3i30000000
χ2722-2-2-12212-2-2-12-2-21-1-12-11112-21-1-2002i−2i00002i2i−2i−2i-1-111000−i3i300−ii0000−i−iii−i3−i3i3i300000000003−30
χ2822-2-2-12212-2-2-12-2-21-1-12-11112-21-1-2002i−2i00002i2i−2i−2i-1-111000i3−i300−ii0000−i−iiii3i3−i3−i30000000000−330
χ2922-2-2-12212-2-2-12-2-21-1-12-11112-21-1-200−2i2i0000−2i−2i2i2i-1-111000−i3i300i−i0000ii−i−i−i3−i3i3i30000000000−330
χ3022-2-2-12212-2-2-12-2-21-1-12-11112-21-1-200−2i2i0000−2i−2i2i2i-1-111000i3−i300i−i0000ii−i−ii3i3−i3−i300000000003−30
χ312-22-2222-2-2-2-2-2-2222222-2-22-2-2-22-220000000000002-22-20000000000000000000002-22-22-20000000
χ322-22-2222-2-2-2-2-2-2222222-2-22-2-2-22-220000000000002-22-2000000000000000000000-22-22-220000000
χ332-22-22-12-211-2-2-22-12-12-1112-211-1-2-10000−i3i3−i3i3−i3i3−i3i3-11-11000000000−i3i3−i3i3−i3i3−i3i300002-2-11-110000000
χ342-22-22-12-211-2-2-22-12-12-1112-211-1-2-10000−i3i3−i3i3i3−i3i3−i3-11-11000000000−i3i3−i3i3i3−i3i3−i30000-221-11-10000000
χ352-22-22-12-211-2-2-22-12-12-1112-211-1-2-10000i3−i3i3−i3−i3i3−i3i3-11-11000000000i3−i3i3−i3−i3i3−i3i30000-221-11-10000000
χ362-22-22-12-211-2-2-22-12-12-1112-211-1-2-10000i3−i3i3−i3i3−i3i3−i3-11-11000000000i3−i3i3−i3i3−i3i3−i300002-2-11-110000000
χ372-2-222222-222-2-2-2-2-2222-22-22-22-2-2-22i−2i002i−2i−2i2i00002-2-2202i−2i0000002i−2i−2i2i000000000000000000000
χ382-2-222222-222-2-2-2-2-2222-22-22-22-2-2-2−2i2i00−2i2i2i−2i00002-2-220−2i2i000000−2i2i2i−2i000000000000000000000
χ392-2-2222-12-22-1-211-2-22-1-1-221-11-1-2112i−2i002i−2i−2i2i0000-111-10−ii003−300−iii−i00003−33−300000000−i3i3000
χ402-2-2222-12-22-1-211-2-22-1-1-221-11-1-2112i−2i002i−2i−2i2i0000-111-10−ii00−3300−iii−i0000−33−3300000000i3−i3000
χ412-2-2222-12-22-1-211-2-22-1-1-221-11-1-211−2i2i00−2i2i2i−2i0000-111-10i−i003−300i−i−ii00003−33−300000000i3−i3000
χ422-2-2222-12-22-1-211-2-22-1-1-221-11-1-211−2i2i00−2i2i2i−2i0000-111-10i−i00−3300i−i−ii0000−33−3300000000−i3i3000
χ432-2-222-1221-12-2-2-21-2-12-11-1-221-11-212i−2i00−iii−i3−3−33-111-102i−2i000000−iii−i3−3−33000000−i3i3i3−i30000000
χ442-2-222-1221-12-2-2-21-2-12-11-1-221-11-212i−2i00−iii−i−333−3-111-102i−2i000000−iii−i−333−3000000i3−i3−i3i30000000
χ452-2-222-1221-12-2-2-21-2-12-11-1-221-11-21−2i2i00i−i−ii3−3−33-111-10−2i2i000000i−i−ii3−3−33000000i3−i3−i3i30000000
χ462-2-222-1221-12-2-2-21-2-12-11-1-221-11-21−2i2i00i−i−ii−333−3-111-10−2i2i000000i−i−ii−333−3000000−i3i3i3−i30000000
χ4744444-2-24-2-2-24-2-2-24-2-21-2-2-2-211-2-214400-2-2-2-2000011110-2-20000001111000000000000000000000
χ4844444-2-24-2-2-24-2-2-24-2-21-2-2-2-211-2-21-4-400222200001111022000000-1-1-1-1000000000000000000000
χ494444-24-2-244-2-2-2-24-2-21-2-2-211-2-2-21-20000000000001111400-2-2-2-2000000000011110000000000000
χ504444-24-2-244-2-2-2-24-2-21-2-2-211-2-2-21-20000000000001111-40022220000000000-1-1-1-10000000000000
χ514444-2-24-2-2-24-244-2-21-2-211-2-2-2-21-2-200440000-2-2-2-211110000000-2-20000111100000000000000000
χ524444-2-24-2-2-24-244-2-21-2-211-2-2-2-21-2-200-4-40000222211110000000220000-1-1-1-100000000000000000
χ5344-4-444-2-44-424-22-4-44-2-24-422-22-4-22000000000000-2-2220000000000000000000000000000000000
χ5444-4-44-2-2-4-2224-222-4-2-21-22221-12-2-100002323−23−23000011-1-1000000000−3−333000000000000000000000
χ5544-4-44-2-2-4-2224-222-4-2-21-22221-12-2-10000−23−232323000011-1-100000000033−3−3000000000000000000000
χ5644-4-4-24-224-42-2-22-42-21-2-22-1-1-2221200000000000011-1-1000−2i32i3000000000000i3i3−i3−i30000000000000
χ5744-4-4-24-224-42-2-22-42-21-2-22-1-1-2221200000000000011-1-10002i3−2i3000000000000−i3−i3i3i30000000000000
χ5844-4-4-2-242-22-4-24-4221-2-21-122-22-1-22004i−4i0000−2i−2i2i2i11-1-10000000−2i2i0000ii−i−i00000000000000000
χ5944-4-4-2-242-22-4-24-4221-2-21-122-22-1-2200−4i4i00002i2i−2i−2i11-1-100000002i−2i0000−i−iii00000000000000000
χ604-44-444-2-4-4-42-42-2444-2-2-4-4-222242-2000000000000-22-220000000000000000000000000000000000
χ614-44-44-2-2-4222-42-2-24-2-2122-22-1-1-2210000−2i32i3−2i32i300001-11-1000000000i3−i3i3−i3000000000000000000000
χ624-44-44-2-2-4222-42-2-24-2-2122-22-1-1-22100002i3−2i32i3−2i300001-11-1000000000−i3i3−i3i3000000000000000000000
χ634-44-4-2442-4-4-42-444-2-2-2422-22-4-4-224000000000000-22-220000000000000000000000000000000000
χ644-44-4-24-22-4-4222-24-2-21-2221-122-2-1-20000000000001-11-1000000000000000003i−3i−3i3i0000000000000
χ654-44-4-24-22-4-4222-24-2-21-2221-122-2-1-20000000000001-11-100000000000000000−3i3i3i−3i0000000000000
χ664-44-4-2-24222-42-44-2-21-2-2-1-1-222212-200000000−2i32i3−2i32i31-11-10000000000000i3−i3i3−i300000000000000000
χ674-44-4-2-24222-42-44-2-21-2-2-1-1-222212-2000000002i3−2i32i3−2i31-11-10000000000000−i3i3−i3i300000000000000000
χ684-4-444-2-242-2-2-4222-4-2-212-22-2-1122-14i−4i00−2i2i2i−2i00001-1-110−2i2i000000i−i−ii000000000000000000000
χ694-4-444-2-242-2-2-4222-4-2-212-22-2-1122-1−4i4i002i−2i−2i2i00001-1-1102i−2i000000−iii−i000000000000000000000
χ704-4-44-244-2-4442-4-4-42-2-242-22-2-4422-4000000000000-222-20000000000000000000000000000000000
χ714-4-44-24-2-2-44-2222-42-21-22-2-112-22-120000000000001-1-110000023−230000000000−33−330000000000000
χ724-4-44-24-2-2-44-2222-42-21-22-2-112-22-120000000000001-1-1100000−232300000000003−33−30000000000000
χ734-4-44-2-24-22-242-4-4221-2-2-112-22-2-1220000000023−23−23231-1-110000000000000−333−300000000000000000
χ744-4-44-2-24-22-242-4-4221-2-2-112-22-2-12200000000−232323−231-1-1100000000000003−3−3300000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-44-444-4-44442222-2-2-22-2-22-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-4444444-4-4-4222-2-22-2-2-22-22000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-4-44-4-444444222-22-22-22-2-2-2000000000000-111-10000000000000000000000000000000000

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