Finite Group Databasebeta

← Group #11723014

Character table — Group #11723014

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order122233366666666633366666666644441212121212121212366641212121212121212121212121212121212121212441212121244121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-11111111-1-111111111-1-1-1-11111-1-1-1-1-1-11-1-1-111-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ51111111111111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1-1
χ61111111111111111111111111111-1-111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1111
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
χ10222222-1222-1-122-122-1-122-1-1-1-12-1-122-2-2-1-1-1-11111-1-1-1-1000-2-20022-1-1-1-111110000-2-211110000000
χ11222222-1222-1-122-122-1-122-1-1-1-12-1-1-2-2221111-1-1-1-1-1-1-1-10002200-2-21111-1-1-1-10000-2-211110000000
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
χ1322222-122-1222-1-122-12-1-1-122-1-1-12-1002200002222-1-1-1-1222-1-1-1-1000000-1-1-1-1-1-1-1-100000002-1-1000
χ1422222-122-1222-1-122-12-1-1-122-1-1-12-1002200002222-1-1-1-1-2-2-2-1-111000000-1-1-1-111110000000-211000
χ1522222-122-1222-1-122-12-1-1-122-1-1-12-100-2-20000-2-2-2-2-1-1-1-122211-1-10000001111-1-1-1-10000000-211000
χ1622222-122-1222-1-122-12-1-1-122-1-1-12-100-2-20000-2-2-2-2-1-1-1-1-2-2-211110000001111111100000002-1-1000
χ172222-122-12-122222-1-1-12-1-1-1-122-1-12220022220000-1-1-1-12-1-10022-1-1-1-1-1-10000-1-1-1-10000002000-1-10
χ182222-122-12-122222-1-1-12-1-1-1-122-1-12220022220000-1-1-1-1-21100-2-2-1-1-1-1-1-100001111000000-2000110
χ192222-122-12-122222-1-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-12-1-100221111110000-1-1-1-1000000-2000110
χ202222-122-12-122222-1-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-1-21100-2-2111111000011110000002000-1-10
χ2122-2-222222-2-2-2-2-22-22222-22-22-2-2-2-200000000000022-2-20000000000000000000002-222-2-20000000
χ2222-2-222222-2-2-2-2-22-22222-22-22-2-2-2-200000000000022-2-2000000000000000000000-22-2-2220000000
χ2322-2-222-122-211-2-2-1-22-1-12-2-11-11-211000033−3−333−3−3-1-11100000000033−3−333−3−300002-2-1-1110000000
χ2422-2-222-122-211-2-2-1-22-1-12-2-11-11-211000033−3−3−3−333-1-11100000000033−3−3−3−3330000-2211-1-10000000
χ2522-2-222-122-211-2-2-1-22-1-12-2-11-11-2110000−3−33333−3−3-1-111000000000−3−33333−3−30000-2211-1-10000000
χ2622-2-222-122-211-2-2-1-22-1-12-2-11-11-2110000−3−333−3−333-1-111000000000−3−333−3−33300002-2-1-1110000000
χ272-22-2222-2-2-22-2-22-22222-22-2-2-22-22-2002i−2i00002i−2i2i−2i2-22-20002i−2i000000002i−2i2i−2i00000000000000000
χ282-22-2222-2-2-22-2-22-22222-22-2-2-22-22-200−2i2i0000−2i2i−2i2i2-22-2000−2i2i00000000−2i2i−2i2i00000000000000000
χ292-22-222-1-2-2-2-11-22122-1-1-22111-1-2-11002i−2i−i3i3−i3i3−ii−ii-11-110002i−2i0000−i3i3−i3i3−ii−ii0000003−33−30000000
χ302-22-222-1-2-2-2-11-22122-1-1-22111-1-2-11002i−2ii3−i3i3−i3−ii−ii-11-110002i−2i0000i3−i3i3−i3−ii−ii000000−33−330000000
χ312-22-222-1-2-2-2-11-22122-1-1-22111-1-2-1100−2i2i−i3i3−i3i3i−ii−i-11-11000−2i2i0000−i3i3−i3i3i−ii−i000000−33−330000000
χ322-22-222-1-2-2-2-11-22122-1-1-22111-1-2-1100−2i2ii3−i3i3−i3i−ii−i-11-11000−2i2i0000i3−i3i3−i3i−ii−i0000003−33−30000000
χ332-22-22-12-21-22-21-1-22-12-11-1-2-21-1121002i−2i00002i−2i2i−2i-11-11000−ii3−3000000−ii−ii33−3−300000000−i3i3000
χ342-22-22-12-21-22-21-1-22-12-11-1-2-21-1121002i−2i00002i−2i2i−2i-11-11000−ii−33000000−ii−ii−3−33300000000i3−i3000
χ352-22-22-12-21-22-21-1-22-12-11-1-2-21-112100−2i2i0000−2i2i−2i2i-11-11000i−i3−3000000i−ii−i33−3−300000000i3−i3000
χ362-22-22-12-21-22-21-1-22-12-11-1-2-21-112100−2i2i0000−2i2i−2i2i-11-11000i−i−33000000i−ii−i−3−33300000000−i3i3000
χ372-2-22222-2-22-222-2-2-2222-2-2-22-2-22-222i−2i002i−2i−2i2i00002-2-2200000002i−2i2i−2i−2i2i000000000000000000000
χ382-2-22222-2-22-222-2-2-2222-2-2-22-2-22-22−2i2i00−2i2i2i−2i00002-2-220000000−2i2i−2i2i2i−2i000000000000000000000
χ392-2-2222-1-2-221-12-21-22-1-1-2-21-11121-12i−2i00−iii−i−i3i3i3−i3-111-100000002i−2i−iii−i−i3i3i3−i3000000−333−30000000
χ402-2-2222-1-2-221-12-21-22-1-1-2-21-11121-12i−2i00−iii−ii3−i3−i3i3-111-100000002i−2i−iii−ii3−i3−i3i30000003−3−330000000
χ412-2-2222-1-2-221-12-21-22-1-1-2-21-11121-1−2i2i00i−i−ii−i3i3i3−i3-111-10000000−2i2ii−i−ii−i3i3i3−i30000003−3−330000000
χ422-2-2222-1-2-221-12-21-22-1-1-2-21-11121-1−2i2i00i−i−iii3−i3−i3i3-111-10000000−2i2ii−i−iii3−i3−i3i3000000−333−30000000
χ432-2-22-1221-2-1-222-2-21-1-12111-1-2-2-1122i−2i002i−2i−2i2i0000-111-10−i3i30000−ii−iii−i0000−i3i3−i3i300000000003−30
χ442-2-22-1221-2-1-222-2-21-1-12111-1-2-2-1122i−2i002i−2i−2i2i0000-111-10i3−i30000−ii−iii−i0000i3−i3i3−i30000000000−330
χ452-2-22-1221-2-1-222-2-21-1-12111-1-2-2-112−2i2i00−2i2i2i−2i0000-111-10−i3i30000i−ii−i−ii0000−i3i3−i3i30000000000−330
χ462-2-22-1221-2-1-222-2-21-1-12111-1-2-2-112−2i2i00−2i2i2i−2i0000-111-10i3−i30000i−ii−i−ii0000i3−i3i3−i300000000003−30
χ4744444-2-24-24-2-2-2-2-24-2-21-2-2-2-211-2-2100440000-2-2-2-21111000-2-200000000111100000000000000000
χ4844444-2-24-24-2-2-2-2-24-2-21-2-2-2-211-2-2100-4-40000222211110002200000000-1-1-1-100000000000000000
χ494444-24-2-24-2-2-244-2-2-21-2-2-211-2-2-21-24400-2-2-2-2000011110000000-2-21111000000000000000000000
χ504444-24-2-24-2-2-244-2-2-21-2-2-211-2-2-21-2-4-400222200001111000000022-1-1-1-1000000000000000000000
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
χ5344-4-44-244-2-4-4-4224-4-24-2-224-4-222-42000000000000-2-2220000000000000000000000000000000000
χ5444-4-44-2-24-2-42222-2-4-2-21-22-221-122-1000000002323−23−2311-1-10000000000000−3−33300000000000000000
χ5544-4-44-2-24-2-42222-2-4-2-21-22-221-122-100000000−23−23232311-1-1000000000000033−3−300000000000000000
χ5644-4-4-244-242-4-4-4-442-2-24-22-224-422-4000000000000-2-2220000000000000000000000000000000000
χ5744-4-4-24-2-24222-4-4-22-21-2-221-1-222-1200002323−23−23000011-1-1000000000−3−333000000000000000000000
χ5844-4-4-24-2-24222-4-4-22-21-2-221-1-222-120000−23−232323000011-1-100000000033−3−3000000000000000000000
χ5944-4-4-2-24-2-22-4-422421-2-21-1-22-22-12200000000000011-1-1000000000000000003i−3i−3i3i0000000000000
χ6044-4-4-2-24-2-22-4-422421-2-21-1-22-22-12200000000000011-1-100000000000000000−3i3i3i−3i0000000000000
χ614-44-44-2-2-42-4-222-224-2-212-222-112-2-1004i−4i0000−2i2i−2i2i1-11-1000−2i2i00000000i−ii−i00000000000000000
χ624-44-44-2-2-42-4-222-224-2-212-222-112-2-100−4i4i00002i−2i2i−2i1-11-10002i−2i00000000−ii−ii00000000000000000
χ634-44-4-2442-424-4-44-4-2-2-242-222-442-2-4000000000000-22-220000000000000000000000000000000000
χ644-44-4-24-22-42-22-442-2-21-22-2-1-12-22120000−2i32i3−2i32i300001-11-1000000000i3−i3i3−i3000000000000000000000
χ654-44-4-24-22-42-22-442-2-21-22-2-1-12-221200002i3−2i32i3−2i300001-11-1000000000−i3i3−i3i3000000000000000000000
χ664-44-4-2-242224-42-2-4-21-2-2-11222-2-1-220000000000001-11-10000023−230000000000−3−3330000000000000
χ674-44-4-2-242224-42-2-4-21-2-2-11222-2-1-220000000000001-11-100000−2323000000000033−3−30000000000000
χ684-4-444-24-424-44-22-4-4-24-222-4422-2-4-2000000000000-222-20000000000000000000000000000000000
χ694-4-444-2-2-4242-2-222-4-2-21222-2-1-1-22100000000−2i32i32i3−2i31-1-110000000000000i3−i3−i3i300000000000000000
χ704-4-444-2-2-4242-2-222-4-2-21222-2-1-1-221000000002i3−2i3−2i32i31-1-110000000000000−i3i3i3−i300000000000000000
χ714-4-44-24-22-4-22-24-422-21-222-1122-2-1-24i−4i00−2i2i2i−2i00001-1-110000000−2i2ii−i−ii000000000000000000000
χ724-4-44-24-22-4-22-24-422-21-222-1122-2-1-2−4i4i002i−2i−2i2i00001-1-1100000002i−2i−iii−i000000000000000000000
χ734-4-44-2-2422-2-44-22-421-2-2-1-12-22212-20000000000001-1-110−2i32i300000000000000i3−i3i3−i30000000000000
χ744-4-44-2-2422-2-44-22-421-2-2-1-12-22212-20000000000001-1-1102i3−2i300000000000000−i3i3−i3i30000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-4-4-444444-442222-22-22-2-2-2-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-4444-444-44-4222-22-2-2-22-22-2000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-444-44-4-4444222-2-2-22-2-22-22000000000000-111-10000000000000000000000000000000000

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