Finite Group Databasebeta

← Group #11723023

Character table — Group #11723023

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order1222333666666666333666666666444412121212121212123666412121212121212121212121212121212121212124412121212246612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-111-1-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-111111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ51111111111111111111111111111-1-111-1-1-1-11111111111111-1-111-1-1-1-111111111-1-1-1-1-1-11-111-1-1-1
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
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
χ9222222-12-122-1-12222-1-122-1-1-1-12-1-1002200002222-1-1-1-12-1-1-1-100220000-1-1-1-1-1-1-1-100000020-1-1000
χ10222222-12-122-1-12222-1-122-1-1-1-12-1-1002200002222-1-1-1-1-2-1-11100-2-20000-1-1-1-11111000000-2011000
χ11222222-12-122-1-12222-1-122-1-1-1-12-1-100-2-20000-2-2-2-2-1-1-1-1211-1-1002200001111-1-1-1-1000000-2011000
χ12222222-12-122-1-12222-1-122-1-1-1-12-1-100-2-20000-2-2-2-2-1-1-1-1-2111100-2-200001111111100000020-1-1000
χ1322222-1222-1-12222-1-12-1-1-122-1-1-12-12222-1-1-1-1-1-1-1-1-1-1-1-1022002200-1-1-1-1-1-1-1-1000022-1-1-1-10000000
χ1422222-1222-1-12222-1-12-1-1-122-1-1-12-122-2-2-1-1-1-11111-1-1-1-10-2-2002200-1-1-1-111110000-2-211110000000
χ1522222-1222-1-12222-1-12-1-1-122-1-1-12-1-2-2221111-1-1-1-1-1-1-1-102200-2-2001111-1-1-1-10000-2-211110000000
χ1622222-1222-1-12222-1-12-1-1-122-1-1-12-1-2-2-2-211111111-1-1-1-10-2-200-2-20011111111000022-1-1-1-10000000
χ172222-122-122222-1-12-1-12-1-1-1-122-1-12220022220000-1-1-1-120022-1-1-1-1-1-1-1-10000-1-1-1-10000000200-1-10
χ182222-122-122222-1-12-1-12-1-1-1-122-1-12220022220000-1-1-1-1-200-2-2-1-111-1-1-1-1000011110000000-200110
χ192222-122-122222-1-12-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-12002211-1-111110000-1-1-1-10000000-200110
χ202222-122-122222-1-12-1-12-1-1-1-122-1-12-2-200-2-2-2-20000-1-1-1-1-200-2-211111111000011110000000200-1-10
χ2122-2-2222-2-22-22-22-2-2222-2-2-2-22-222-200000000000022-2-20000000000000000000002i−2i2i2i−2i−2i0000000
χ2222-2-2222-2-22-22-22-2-2222-2-2-2-22-222-200000000000022-2-2000000000000000000000−2i2i−2i−2i2i2i0000000
χ2322-2-22-12-2-2-112-22-21-12-111-2-2-11-1210000−i3−i3i3i333−3−3-1-111000000000−i3−i3i3i333−3−300002i−2i−i−iii0000000
χ2422-2-22-12-2-2-112-22-21-12-111-2-2-11-1210000−i3−i3i3i3−3−333-1-111000000000−i3−i3i3i3−3−3330000−2i2iii−i−i0000000
χ2522-2-22-12-2-2-112-22-21-12-111-2-2-11-1210000i3i3−i3−i333−3−3-1-111000000000i3i3−i3−i333−3−30000−2i2iii−i−i0000000
χ2622-2-22-12-2-2-112-22-21-12-111-2-2-11-1210000i3i3−i3−i3−3−333-1-111000000000i3i3−i3−i3−3−33300002i−2i−i−iii0000000
χ272-22-2222-2-2-22-22-22-22222-22-2-2-2-2-222i−2i002i−2i2i−2i00002-22-2000002i−2i002i−2i2i−2i000000000000000000000
χ282-22-2222-2-2-22-22-22-22222-22-2-2-2-2-22−2i2i00−2i2i−2i2i00002-22-200000−2i2i00−2i2i−2i2i000000000000000000000
χ292-22-22-12-2-21-1-22-221-12-1-112-2111-2-12i−2i00−ii−ii−i3i3−i3i3-11-11000002i−2i00−ii−ii−i3i3−i3i30000003−33−30000000
χ302-22-22-12-2-21-1-22-221-12-1-112-2111-2-12i−2i00−ii−iii3−i3i3−i3-11-11000002i−2i00−ii−iii3−i3i3−i3000000−33−330000000
χ312-22-22-12-2-21-1-22-221-12-1-112-2111-2-1−2i2i00i−ii−i−i3i3−i3i3-11-1100000−2i2i00i−ii−i−i3i3−i3i3000000−33−330000000
χ322-22-22-12-2-21-1-22-221-12-1-112-2111-2-1−2i2i00i−ii−ii3−i3i3−i3-11-1100000−2i2i00i−ii−ii3−i3i3−i30000003−33−30000000
χ332-22-2-1221-2-22-221-1-2-1-12-11-11-2-21122i−2i002i−2i2i−2i0000-11-1100000−ii3−3−ii−ii000033−3−30000000000−i3i30
χ342-22-2-1221-2-22-221-1-2-1-12-11-11-2-21122i−2i002i−2i2i−2i0000-11-1100000−ii−33−ii−ii0000−3−3330000000000i3−i30
χ352-22-2-1221-2-22-221-1-2-1-12-11-11-2-2112−2i2i00−2i2i−2i2i0000-11-1100000i−i3−3i−ii−i000033−3−30000000000i3−i30
χ362-22-2-1221-2-22-221-1-2-1-12-11-11-2-2112−2i2i00−2i2i−2i2i0000-11-1100000i−i−33i−ii−i0000−3−3330000000000−i3i30
χ372-2-2222222-2-2-2-2-2-22222-22-22-22-2-2-2002i−2i00002i−2i−2i2i2-2-2202i−2i00000000002i−2i−2i2i00000000000000000
χ382-2-2222222-2-2-2-2-2-22222-22-22-22-2-2-200−2i2i0000−2i2i2i−2i2-2-220−2i2i0000000000−2i2i2i−2i00000000000000000
χ392-2-2222-12-1-2-211-2-222-1-1-221-11-1-211002i−2i00002i−2i−2i2i-111-10−ii3−300000000−iii−i3−33−300000000−i3i3000
χ402-2-2222-12-1-2-211-2-222-1-1-221-11-1-211002i−2i00002i−2i−2i2i-111-10−ii−3300000000−iii−i−33−3300000000i3−i3000
χ412-2-2222-12-1-2-211-2-222-1-1-221-11-1-21100−2i2i0000−2i2i2i−2i-111-10i−i3−300000000i−i−ii3−33−300000000i3−i3000
χ422-2-2222-12-1-2-211-2-222-1-1-221-11-1-21100−2i2i0000−2i2i2i−2i-111-10i−i−3300000000i−i−ii−33−3300000000−i3i3000
χ432-2-222-122211-2-2-2-2-1-12-11-1-221-11-21002i−2i3−3−33−iii−i-111-102i−2i0000003−3−33−iii−i000000i3−i3−i3i30000000
χ442-2-222-122211-2-2-2-2-1-12-11-1-221-11-21002i−2i−333−3−iii−i-111-102i−2i000000−333−3−iii−i000000−i3i3i3−i30000000
χ452-2-222-122211-2-2-2-2-1-12-11-1-221-11-2100−2i2i3−3−33i−i−ii-111-10−2i2i0000003−3−33i−i−ii000000−i3i3i3−i30000000
χ462-2-222-122211-2-2-2-2-1-12-11-1-221-11-2100−2i2i−333−3i−i−ii-111-10−2i2i000000−333−3i−i−ii000000i3−i3−i3i30000000
χ4744444-2-24-2-2-2-2-244-2-2-21-2-2-2-211-2-2100440000-2-2-2-211110-2-20000000000111100000000000000000
χ4844444-2-24-2-2-2-2-244-2-2-21-2-2-2-211-2-2100-4-40000222211110220000000000-1-1-1-100000000000000000
χ494444-24-2-2-244-2-2-2-24-21-2-2-211-2-2-21-20000000000001111400-2-200-2-20000000011110000000000000
χ504444-24-2-2-244-2-2-2-24-21-2-2-211-2-2-21-20000000000001111-40022002200000000-1-1-1-10000000000000
χ514444-2-24-24-2-244-2-2-21-2-211-2-2-2-21-2-24400-2-2-2-20000111100000-2-2001111000000000000000000000
χ524444-2-24-24-2-244-2-2-21-2-211-2-2-2-21-2-2-4-400222200001111000002200-1-1-1-1000000000000000000000
χ5344-4-444-2-424-4-224-4-44-2-2-4-422-224-22000000000000-2-2220000000000000000000000000000000000
χ5444-4-44-2-2-42-22-224-42-2-2122221-1-2-2-1000000002323−23−2311-1-10000000000000−3−33300000000000000000
χ5544-4-44-2-2-42-22-224-42-2-2122221-1-2-2-100000000−23−23232311-1-1000000000000033−3−300000000000000000
χ5644-4-4-2442-44-44-4-22-4-2-2422224-4-2-2-4000000000000-2-2220000000000000000000000000000000000
χ5744-4-4-24-2224-4-22-22-4-21-222-1-1-22-21200000000000011-1-1000000000000000003-3-330000000000000
χ5844-4-4-24-2224-4-22-22-4-21-222-1-1-22-21200000000000011-1-100000000000000000-333-30000000000000
χ5944-4-4-2-242-4-224-4-2221-2-2-1-122-221-220000−2i3−2i32i32i3000011-1-1000000000i3i3−i3−i3000000000000000000000
χ6044-4-4-2-242-4-224-4-2221-2-2-1-122-221-2200002i32i3−2i3−2i3000011-1-1000000000−i3−i3i3i3000000000000000000000
χ614-44-444-2-42-442-2-44-44-2-24-4-2222-42-2000000000000-22-220000000000000000000000000000000000
χ624-44-44-2-2-422-22-2-442-2-21-22-22-1-122100000000−2i32i3−2i32i31-11-10000000000000i3−i3i3−i300000000000000000
χ634-44-44-2-2-422-22-2-442-2-21-22-22-1-1221000000002i3−2i32i3−2i31-11-10000000000000−i3i3−i3i300000000000000000
χ644-44-4-24-222-442-22-2-4-21-2-221-1222-1-20000000000001-11-1000000023−2300000000−3−3330000000000000
χ654-44-4-24-222-442-22-2-4-21-2-221-1222-1-20000000000001-11-10000000−23230000000033−3−30000000000000
χ664-44-4-2-242-42-2-442-221-2-21-1-2222-12-24i−4i00−2i2i−2i2i00001-11-100000−2i2i00i−ii−i000000000000000000000
χ674-44-4-2-242-42-2-442-221-2-21-1-2222-12-2−4i4i002i−2i2i−2i00001-11-1000002i−2i00−ii−ii000000000000000000000
χ684-4-444-2-24-22222-4-4-2-2-212-22-2-1122-1004i−4i0000−2i2i2i−2i1-1-110−2i2i0000000000i−i−ii00000000000000000
χ694-4-444-2-24-22222-4-4-2-2-212-22-2-1122-100−4i4i00002i−2i−2i2i1-1-1102i−2i0000000000−iii−i00000000000000000
χ704-4-44-244-24-4-4-4-4224-2-242-22-2-4422-4000000000000-222-20000000000000000000000000000000000
χ714-4-44-24-2-2-2-4-422224-21-22-2-112-22-120000000000001-1-1100023−23000000000000−33−330000000000000
χ724-4-44-24-2-2-2-4-422224-21-22-2-112-22-120000000000001-1-11000−23230000000000003−33−30000000000000
χ734-4-44-2-24-2422-4-422-21-2-2-112-22-2-122000023−23−232300001-1-11000000000−333−3000000000000000000000
χ744-4-44-2-24-2422-4-422-21-2-2-112-22-2-1220000−232323−2300001-1-110000000003−3−33000000000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-444-44-44-444222-2-2-2-22-222-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-4444-44-44-442222-22-2-2-2-2-22000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-4-4-4444444-4222-22-22-22-2-2-2000000000000-111-10000000000000000000000000000000000

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