Finite Group Databasebeta

← Group #11722978

Character table — Group #11722978

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order12223336666666663336666666662244666612121212366646666661212121212121212121212121212441212121244121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-1-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111-1-111-1-1-1-1111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1-111-1
χ61111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111-1-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-11
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
χ9222222-1222-12-1-1222-1-122-1-1-1-1-12-1220022220000-1-1-1-12-1-1-1-1-1-122-1-1000000-1-1-1-100000020-1-1000
χ10222222-1222-12-1-1222-1-122-1-1-1-1-12-1220022220000-1-1-1-1-2-1-1-1-1-1-1-2-2110000001111000000-2011000
χ11222222-1222-12-1-1222-1-122-1-1-1-1-12-1-2-200-2-2-2-20000-1-1-1-1211111122-1-1000000-1-1-1-1000000-2011000
χ12222222-1222-12-1-1222-1-122-1-1-1-1-12-1-2-200-2-2-2-20000-1-1-1-1-2111111-2-211000000111100000020-1-1000
χ1322222-122-1-122222-1-12-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1022-1-1-1-1000022-1-1-1-1000022-1-1-1-10000000
χ1422222-122-1-122222-1-12-1-1-122-1-1-1-1222-2-2-1-1-1-11111-1-1-1-1022-1-1-1-10000-2-211110000-2-211110000000
χ1522222-122-1-122222-1-12-1-1-122-1-1-1-12-2-2221111-1-1-1-1-1-1-1-10-2-21111000022-1-1-1-10000-2-211110000000
χ1622222-122-1-122222-1-12-1-1-122-1-1-1-12-2-2-2-211111111-1-1-1-10-2-211110000-2-21111000022-1-1-1-10000000
χ172222-122-1222-122-12-1-12-1-1-1-1222-1-1002200002222-1-1-1-12000000-1-122-1-1-1-1-1-1-1-1-1-10000000200-1-10
χ182222-122-1222-122-12-1-12-1-1-1-1222-1-1002200002222-1-1-1-1-200000011-2-2-1-1-1-1-1-111110000000-200110
χ192222-122-1222-122-12-1-12-1-1-1-1222-1-100-2-20000-2-2-2-2-1-1-1-12000000-1-122111111-1-1-1-10000000-200110
χ202222-122-1222-122-12-1-12-1-1-1-1222-1-100-2-20000-2-2-2-2-1-1-1-1-200000011-2-211111111110000000200-1-10
χ2122-2-222222-22-2-2-2-2-22222-22-22-2-2-2-22-20022-2-2000022-2-202-222-2-2000000000000000000000000000
χ2222-2-222222-22-2-2-2-2-22222-22-22-2-2-2-2-2200-2-222000022-2-20-22-2-222000000000000000000000000000
χ2322-2-222-122-2-1-211-2-22-1-12-2-11-111-212-20022-2-20000-1-1110-11-1-111003−300000033−3−3000000003−3000
χ2422-2-222-122-2-1-211-2-22-1-12-2-11-111-212-20022-2-20000-1-1110-11-1-11100−33000000−3−33300000000−33000
χ2522-2-222-122-2-1-211-2-22-1-12-2-11-111-21-2200-2-2220000-1-11101-111-1-1003−300000033−3−300000000−33000
χ2622-2-222-122-2-1-211-2-22-1-12-2-11-111-21-2200-2-2220000-1-11101-111-1-100−33000000−3−333000000003−3000
χ2722-2-22-122-112-2-2-2-21-12-1-112-2-1111-22-200-1-11133−3−3-1-11102-2-1-11100000033−3−300000033−3−30000000
χ2822-2-22-122-112-2-2-2-21-12-1-112-2-1111-22-200-1-111−3−333-1-11102-2-1-111000000−3−333000000−3−3330000000
χ2922-2-22-122-112-2-2-2-21-12-1-112-2-1111-2-220011-1-133−3−3-1-1110-2211-1-100000033−3−3000000−3−3330000000
χ3022-2-22-122-112-2-2-2-21-12-1-112-2-1111-2-220011-1-1−3−333-1-1110-2211-1-1000000−3−33300000033−3−30000000
χ312-22-2222-2-22-222-2-2-2222-22-2-2-22-2-22002i−2i00002i−2i2i−2i2-22-2000000000002i−2i2i−2i2i−2i00000000000000000
χ322-22-2222-2-22-222-2-2-2222-22-2-2-22-2-2200−2i2i0000−2i2i−2i2i2-22-200000000000−2i2i−2i2i−2i2i00000000000000000
χ332-22-22-12-21-1-222-2-21-12-11-1-2-21-1112002i−2i−i3i3−i3i3−ii−ii-11-11000−i3i3−i3i300002i−2i−ii−ii0000003−33−30000000
χ342-22-22-12-21-1-222-2-21-12-11-1-2-21-1112002i−2ii3−i3i3−i3−ii−ii-11-11000i3−i3i3−i300002i−2i−ii−ii000000−33−330000000
χ352-22-22-12-21-1-222-2-21-12-11-1-2-21-111200−2i2i−i3i3−i3i3i−ii−i-11-11000−i3i3−i3i30000−2i2ii−ii−i000000−33−330000000
χ362-22-22-12-21-1-222-2-21-12-11-1-2-21-111200−2i2ii3−i3i3−i3i−ii−i-11-11000i3−i3i3−i30000−2i2ii−ii−i0000003−33−30000000
χ372-22-2-1221-22-2-12-21-2-1-121-111-22-21-1002i−2i00002i−2i2i−2i-11-110000000−i3i300−ii−ii−ii−i3i3−i3i300000000003−30
χ382-22-2-1221-22-2-12-21-2-1-121-111-22-21-1002i−2i00002i−2i2i−2i-11-110000000i3−i300−ii−ii−iii3−i3i3−i30000000000−330
χ392-22-2-1221-22-2-12-21-2-1-121-111-22-21-100−2i2i0000−2i2i−2i2i-11-110000000−i3i300i−ii−ii−i−i3i3−i3i30000000000−330
χ402-22-2-1221-22-2-12-21-2-1-121-111-22-21-100−2i2i0000−2i2i−2i2i-11-110000000i3−i300i−ii−ii−ii3−i3i3−i300000000003−30
χ412-2-22222-2-2-2-2-2-2222222-2-2-22-2-222-20000000000002-2-220000000000000000000002-22-2-220000000
χ422-2-22222-2-2-2-2-2-2222222-2-2-22-2-222-20000000000002-2-22000000000000000000000-22-222-20000000
χ432-2-222-12-211-2-2-222-1-12-111-2211-1-1-20000−i3i3i3−i3−i3i3i3−i3-111-1000−i3i3i3−i3000000−i3i3i3−i300002-2-111-10000000
χ442-2-222-12-211-2-2-222-1-12-111-2211-1-1-20000−i3i3i3−i3i3−i3−i3i3-111-1000−i3i3i3−i3000000i3−i3−i3i30000-221-1-110000000
χ452-2-222-12-211-2-2-222-1-12-111-2211-1-1-20000i3−i3−i3i3−i3i3i3−i3-111-1000i3−i3−i3i3000000−i3i3i3−i30000-221-1-110000000
χ462-2-222-12-211-2-2-222-1-12-111-2211-1-1-20000i3−i3−i3i3i3−i3−i3i3-111-1000i3−i3−i3i3000000i3−i3−i3i300002-2-111-10000000
χ4744444-2-24-2-2-24-2-24-2-2-21-2-2-2-2111-2-24400-2-2-2-2000011110-2-21111000000000000000000000000000
χ4844444-2-24-2-2-24-2-24-2-2-21-2-2-2-2111-2-2-4-400222200001111022-1-1-1-1000000000000000000000000000
χ494444-24-2-244-2-2-2-2-24-21-2-2-211-2-2-2-2100000000000011114000000-2-2-2-200000011110000000000000
χ504444-24-2-244-2-2-2-2-24-21-2-2-211-2-2-2-210000000000001111-40000002222000000-1-1-1-10000000000000
χ514444-2-24-2-2-24-244-2-21-2-211-2-2-2-2-21-200440000-2-2-2-2111100000000000-2-2111100000000000000000
χ524444-2-24-2-2-24-244-2-21-2-211-2-2-2-2-21-200-4-40000222211110000000000022-1-1-1-100000000000000000
χ5344-4-44-2-24-22-2-422-42-2-21-22-221-1-1224-400-2-222000011-1-10-2211-1-1000000000000000000000000000
χ5444-4-44-2-24-22-2-422-42-2-21-22-221-1-122-440022-2-2000011-1-102-2-1-111000000000000000000000000000
χ5544-4-4-244-24-442-4-42-4-2-24-22-224-4-422000000000000-2-2220000000000000000000000000000000000
χ5644-4-4-24-2-24-4-22222-4-21-2-221-1-2222-100000000000011-1-100000000023−23000000−3−3330000000000000
χ5744-4-4-24-2-24-4-22222-4-21-2-221-1-2222-100000000000011-1-1000000000−232300000033−3−30000000000000
χ5844-4-4-2-24-2-2242-4-4221-2-21-1-22-222-12000000002323−23−2311-1-10000000000000−3−33300000000000000000
χ5944-4-4-2-24-2-2242-4-4221-2-21-1-22-222-1200000000−23−23232311-1-1000000000000033−3−300000000000000000
χ604-44-444-2-4-4424-22-4-44-2-2-44222-22-4-2000000000000-22-220000000000000000000000000000000000
χ614-44-44-2-2-42-224-22-42-2-212-222-11-12-20000−2i32i3−2i32i300001-11-1000i3−i3i3−i3000000000000000000000000000
χ624-44-44-2-2-42-224-22-42-2-212-222-11-12-200002i3−2i32i3−2i300001-11-1000−i3i3−i3i3000000000000000000000000000
χ634-44-4-24-22-442-2-222-4-21-22-2-1-12-22210000000000001-11-10000000−2i32i300000000i3−i3i3−i30000000000000
χ644-44-4-24-22-442-2-222-4-21-22-2-1-12-22210000000000001-11-100000002i3−2i300000000−i3i3−i3i30000000000000
χ654-44-4-2-2422-2-4-24-4221-2-2-11222-22-1-2004i−4i0000−2i2i−2i2i1-11-100000000000−2i2ii−ii−i00000000000000000
χ664-44-4-2-2422-2-4-24-4221-2-2-11222-22-1-200−4i4i00002i−2i2i−2i1-11-1000000000002i−2i−ii−ii00000000000000000
χ674-4-4444-2-4-4-42-42-2444-2-2-4-42-222-242000000000000-222-20000000000000000000000000000000000
χ684-4-444-2-2-4222-42-24-2-2-21222-2-1-11-220000−2i32i32i3−2i300001-1-11000i3−i3−i3i3000000000000000000000000000
χ694-4-444-2-2-4222-42-24-2-2-21222-2-1-11-2200002i3−2i3−2i32i300001-1-11000−i3i3i3−i3000000000000000000000000000
χ704-4-44-2442-4-4-42-44-24-2-24222-2-4-44-22000000000000-222-20000000000000000000000000000000000
χ714-4-44-24-22-4-4222-2-24-21-222-1122-2-2-10000000000001-1-11000000000000000003i−3i−3i3i0000000000000
χ724-4-44-24-22-4-4222-2-24-21-222-1122-2-2-10000000000001-1-1100000000000000000−3i3i3i−3i0000000000000
χ734-4-44-2-24222-42-44-2-21-2-2-1-12-222-21200000000−2i32i32i3−2i31-1-110000000000000i3−i3−i3i300000000000000000
χ744-4-44-2-24222-42-44-2-21-2-2-1-12-222-212000000002i3−2i3−2i32i31-1-110000000000000−i3i3i3−i300000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-4-4-44-4444442222-22-22-2-2-2-2000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-444-44-4-4444222-22-2-2-22-2-22000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-4444444-4-4-4222-2-2-22-2-222-2000000000000-111-10000000000000000000000000000000000

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