Finite Group Databasebeta

← Group #11723021

Character table — Group #11723021

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order122233366666666633366666666644441212121212121212366641212121212121212121212121212121212121212441212121244121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111
χ51111111111111111111111111111-1-111-1-1-1-111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-11-1-1-111-1
χ61111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
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
χ9222222-1222-1-122-122-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000220022-1-1-1-1-1-1-1-1000022-1-1-1-10000000
χ10222222-1222-1-122-122-1-122-1-1-1-12-1-122-2-2-1-1-1-11111-1-1-1-10002200-2-2-1-1-1-111110000-2-211110000000
χ11222222-1222-1-122-122-1-122-1-1-1-12-1-1-2-2221111-1-1-1-1-1-1-1-1000-2-200221111-1-1-1-10000-2-211110000000
χ12222222-1222-1-122-122-1-122-1-1-1-12-1-1-2-2-2-211111111-1-1-1-1000-2-200-2-211111111000022-1-1-1-10000000
χ1322222-122-1222-1-122-12-1-1-122-1-1-12-1220022220000-1-1-1-1222-1-1-1-100-1-1-1-10000-1-1-1-100000002-1-1000
χ1422222-122-1222-1-122-12-1-1-122-1-1-12-1220022220000-1-1-1-1-2-2-2-1-11100-1-1-1-1000011110000000-211000
χ1522222-122-1222-1-122-12-1-1-122-1-1-12-1-2-200-2-2-2-20000-1-1-1-122211-1-10011110000-1-1-1-10000000-211000
χ1622222-122-1222-1-122-12-1-1-122-1-1-12-1-2-200-2-2-2-20000-1-1-1-1-2-2-211110011110000111100000002-1-1000
χ172222-122-12-122222-1-1-12-1-1-1-122-1-12002200002222-1-1-1-12-1-10022-1-10000-1-1-1-1-1-1-1-10000002000-1-10
χ182222-122-12-122222-1-1-12-1-1-1-122-1-12002200002222-1-1-1-1-21100-2-2-1-10000-1-1-1-11111000000-2000110
χ192222-122-12-122222-1-1-12-1-1-1-122-1-1200-2-20000-2-2-2-2-1-1-1-12-1-100221100001111-1-1-1-1000000-2000110
χ202222-122-12-122222-1-1-12-1-1-1-122-1-1200-2-20000-2-2-2-2-1-1-1-1-21100-2-2110000111111110000002000-1-10
χ2122-2-2222-2-222-22-2-2-2222-2-22-2-2-22-22002i−2i00002i2i−2i−2i22-2-200000002i−2i00002i2i−2i−2i00000000000000000
χ2222-2-2222-2-222-22-2-2-2222-2-22-2-2-22-2200−2i2i0000−2i−2i2i2i22-2-20000000−2i2i0000−2i−2i2i2i00000000000000000
χ2322-2-222-1-2-22-112-21-22-1-1-2-2-111121-1002i−2i−i3−i3i3i3−i−iii-1-11100000002i−2i−i3−i3i3i3−i−iii00000033−3−30000000
χ2422-2-222-1-2-22-112-21-22-1-1-2-2-111121-1002i−2ii3i3−i3−i3−i−iii-1-11100000002i−2ii3i3−i3−i3−i−iii000000−3−3330000000
χ2522-2-222-1-2-22-112-21-22-1-1-2-2-111121-100−2i2i−i3−i3i3i3ii−i−i-1-1110000000−2i2i−i3−i3i3i3ii−i−i000000−3−3330000000
χ2622-2-222-1-2-22-112-21-22-1-1-2-2-111121-100−2i2ii3i3−i3−i3ii−i−i-1-1110000000−2i2ii3i3−i3−i3ii−i−i00000033−3−30000000
χ2722-2-2-1221-2-12-22-2-21-1-1211-11-2-2-112002i−2i00002i2i−2i−2i-1-1110−i3i30000−ii0000−i−iii−i3−i3i3i300000000003−30
χ2822-2-2-1221-2-12-22-2-21-1-1211-11-2-2-112002i−2i00002i2i−2i−2i-1-1110i3−i30000−ii0000−i−iiii3i3−i3−i30000000000−330
χ2922-2-2-1221-2-12-22-2-21-1-1211-11-2-2-11200−2i2i0000−2i−2i2i2i-1-1110−i3i30000i−i0000ii−i−i−i3−i3i3i30000000000−330
χ3022-2-2-1221-2-12-22-2-21-1-1211-11-2-2-11200−2i2i0000−2i−2i2i2i-1-1110i3−i30000i−i0000ii−i−ii3i3−i3−i300000000003−30
χ312-22-2222-22-2-22-2-2-222222-2-2-22-2-22-20000000000002-22-20000000000000000000002i−2i2i−2i2i−2i0000000
χ322-22-2222-22-2-22-2-2-222222-2-2-22-2-22-20000000000002-22-2000000000000000000000−2i2i−2i2i−2i2i0000000
χ332-22-222-1-22-21-1-2-2122-1-12-211-11-2-1100003−33−3−i3i3−i3i3-11-110000000003−33−3−i3i3−i3i300002i−2i−ii−ii0000000
χ342-22-222-1-22-21-1-2-2122-1-12-211-11-2-1100003−33−3i3−i3i3−i3-11-110000000003−33−3i3−i3i3−i30000−2i2ii−ii−i0000000
χ352-22-222-1-22-21-1-2-2122-1-12-211-11-2-110000−33−33−i3i3−i3i3-11-11000000000−33−33−i3i3−i3i30000−2i2ii−ii−i0000000
χ362-22-222-1-22-21-1-2-2122-1-12-211-11-2-110000−33−33i3−i3i3−i3-11-11000000000−33−33i3−i3i3−i300002i−2i−ii−ii0000000
χ372-2-222222-2-2-2-2-222-2222-22-22-22-2-2-22i−2i002i−2i−2i2i00002-2-220002i−2i00002i−2i−2i2i000000000000000000000
χ382-2-222222-2-2-2-2-222-2222-22-22-22-2-2-2−2i2i00−2i2i2i−2i00002-2-22000−2i2i0000−2i2i2i−2i000000000000000000000
χ392-2-2222-12-2-211-22-1-22-1-1-221-11-1-2112i−2i00−iii−i3−3−33-111-10002i−2i0000−iii−i3−3−33000000i3−i3−i3i30000000
χ402-2-2222-12-2-211-22-1-22-1-1-221-11-1-2112i−2i00−iii−i−333−3-111-10002i−2i0000−iii−i−333−3000000−i3i3i3−i30000000
χ412-2-2222-12-2-211-22-1-22-1-1-221-11-1-211−2i2i00i−i−ii3−3−33-111-1000−2i2i0000i−i−ii3−3−33000000−i3i3i3−i30000000
χ422-2-2222-12-2-211-22-1-22-1-1-221-11-1-211−2i2i00i−i−ii−333−3-111-1000−2i2i0000i−i−ii−333−3000000i3−i3−i3i30000000
χ432-2-222-1221-2-2-21-12-2-12-11-1-221-11-212i−2i002i−2i−2i2i0000-111-1000−ii3−300−iii−i00003−33−300000000−i3i3000
χ442-2-222-1221-2-2-21-12-2-12-11-1-221-11-212i−2i002i−2i−2i2i0000-111-1000−ii−3300−iii−i0000−33−3300000000i3−i3000
χ452-2-222-1221-2-2-21-12-2-12-11-1-221-11-21−2i2i00−2i2i2i−2i0000-111-1000i−i3−300i−i−ii00003−33−300000000i3−i3000
χ462-2-222-1221-2-2-21-12-2-12-11-1-221-11-21−2i2i00−2i2i2i−2i0000-111-1000i−i−3300i−i−ii0000−33−3300000000−i3i3000
χ4744444-2-24-24-2-2-2-2-24-2-21-2-2-2-211-2-214400-2-2-2-200001111000-2-200001111000000000000000000000
χ4844444-2-24-24-2-2-2-2-24-2-21-2-2-2-211-2-21-4-400222200001111000220000-1-1-1-1000000000000000000000
χ494444-24-2-24-2-2-244-2-2-21-2-2-211-2-2-21-200440000-2-2-2-211110000000-2-20000111100000000000000000
χ504444-24-2-24-2-2-244-2-2-21-2-2-211-2-2-21-200-4-40000222211110000000220000-1-1-1-100000000000000000
χ514444-2-24-2-2-244-2-24-21-2-211-2-2-2-21-2-200000000000011114-2-200-2-2000000000011110000000000000
χ524444-2-24-2-2-244-2-24-21-2-211-2-2-2-21-2-20000000000001111-42200220000000000-1-1-1-10000000000000
χ5344-4-44-24-4244-4-22-4-4-24-2224-422-2-4-2000000000000-2-2220000000000000000000000000000000000
χ5444-4-44-2-2-424-22-222-4-2-2122-22-1-1-2210000−2i3−2i32i32i3000011-1-1000000000i3i3−i3−i3000000000000000000000
χ5544-4-44-2-2-424-22-222-4-2-2122-22-1-1-22100002i32i3−2i3−2i3000011-1-1000000000−i3−i3i3i3000000000000000000000
χ5644-4-4-24-22-4-2-224-422-21-2221-122-2-1-2004i−4i0000−2i−2i2i2i11-1-10000000−2i2i0000ii−i−i00000000000000000
χ5744-4-4-24-22-4-2-224-422-21-2221-122-2-1-200−4i4i00002i2i−2i−2i11-1-100000002i−2i0000−i−iii00000000000000000
χ5844-4-4-2-2422-24-4-22-421-2-2-1-1-222212-200000000000011-1-10−2i32i300000000000000i3i3−i3−i30000000000000
χ5944-4-4-2-2422-24-4-22-421-2-2-1-1-222212-200000000000011-1-102i3−2i300000000000000−i3−i3i3i30000000000000
χ604-44-44-24-4-2-4-4422-44-24-2-22-4-4-22242000000000000-22-220000000000000000000000000000000000
χ614-44-44-2-2-4-2-42-22224-2-21-22221-12-2-1000023−2323−2300001-11-1000000000−33−33000000000000000000000
χ624-44-44-2-2-4-2-42-22224-2-21-22221-12-2-10000−2323−232300001-11-10000000003−33−3000000000000000000000
χ634-44-4-244242-44-4-4-4-2-2-24-22224-42-2-4000000000000-22-220000000000000000000000000000000000
χ644-44-4-24-22422-2-4-42-2-21-2-22-1-1-2221200000000−2i32i3−2i32i31-11-10000000000000i3−i3i3−i300000000000000000
χ654-44-4-24-22422-2-4-42-2-21-2-22-1-1-22212000000002i3−2i32i3−2i31-11-10000000000000−i3i3−i3i300000000000000000
χ664-44-4-2-242-22-4422-4-21-2-21-122-22-1-220000000000001-11-1000000000000000003i−3i−3i3i0000000000000
χ674-44-4-2-242-22-4422-4-21-2-21-122-22-1-220000000000001-11-100000000000000000−3i3i3i−3i0000000000000
χ684-4-444-2-242-4222-2-2-4-2-212-22-2-1122-14i−4i00−2i2i2i−2i00001-1-11000−2i2i0000i−i−ii000000000000000000000
χ694-4-444-2-242-4222-2-2-4-2-212-22-2-1122-1−4i4i002i−2i−2i2i00001-1-110002i−2i0000−iii−i000000000000000000000
χ704-4-44-244-2-42-4-4-4442-2-242-22-2-4422-4000000000000-222-20000000000000000000000000000000000
χ714-4-44-24-2-2-4222-44-22-21-22-2-112-22-120000000023−23−23231-1-110000000000000−333−300000000000000000
χ724-4-44-24-2-2-4222-44-22-21-22-2-112-22-1200000000−232323−231-1-1100000000000003−3−3300000000000000000
χ734-4-44-2-24-222-4-42-2421-2-2-112-22-2-1220000000000001-1-110000023−230000000000−33−330000000000000
χ744-4-44-2-24-222-4-42-2421-2-2-112-22-2-1220000000000001-1-1100000−232300000000003−33−30000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-444-4-44-4444222-2-22-2-2-22-22000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-44-444-4444-42222-2-2-22-2-22-2000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-4-444444-4-44222-22-22-22-2-2-2000000000000-111-10000000000000000000000000000000000

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