Finite Group Databasebeta

← Group #72220778

Character table — Group #72220778

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112444444448888888888881212161616161616161616161616181818182424242424242424242436363636363636364848484848484848727272728181108108108108108108162216216216216216216324324324324
order12233336666333366666666243366666666662222666661212121212666666666666121212126666222444442612121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111-1-1-1-111111111-111-1-1-1-1-1ii−i−i-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111111-1-111111111111111-1-1-1-111111111-111-1-1-1-1-1−i−iii-1-1-1−i−iii−i−iii
χ511111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111-1-11111-1-1-1-1
χ611111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111
χ711111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111ii−i−i-111ii−i−i−i−iii
χ811111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111−i−iii-111−i−iiiii−i−i
χ911-1111111111111-1-1-1-111111-111-1-1-1-111-1-1-1-11-11-111111-1-1-1-1-1111111-1-11111-1-1-1-11-1-1-1111-1i−ii−i-11-1i−ii−ii−ii−i
χ1011-1111111111111-1-1-1-111111-111-1-1-1-111-1-1-1-11-11-111111-1-1-1-1-1111111-1-11111-1-1-1-11-1-1-1111-1−ii−ii-11-1−ii−ii−ii−ii
χ1111-1111111111111-1-1-1-111111-111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-1-1-111-1-111-111-1-111-1-11
χ1211-1111111111111-1-1-1-111111-111-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-1-1-11-111-11-11-111-1-111-1
χ1311-1111111111111-1-1-1-11111-1111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-111111111111-1-1-1-1-1-111111-1-1-111-11i−ii−i-1-11i−ii−i−ii−ii
χ1411-1111111111111-1-1-1-11111-1111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-111111111111-1-1-1-1-1-111111-1-1-111-11−ii−ii-1-11−ii−iii−ii−i
χ1511-1111111111111-1-1-1-11111-1111-1-1-1-111-1-1-1-11-1-11-1-1-1-1-1111111111-1-111-1-1-1-11111-1-1-11-1-11-11-1-1111-11-1-11-111-1
χ1611-1111111111111-1-1-1-11111-1111-1-1-1-111-1-1-1-11-1-11-1-1-1-1-1111111111-1-111-1-1-1-11111-1-1-11-1-11-1-111-111-1-111-11-1-11
χ172222222222222222222222200222222222222-2-2220000000000-2-2-2-22222000000002-2-22-2-2000000-20000000000
χ182222222222222222222222200222222222222-2-2-2-20000000000-2-2-2-2-2-2-2-200000000-2-2-2-22200000020000000000
χ1922-2222222222222-2-2-2-222220022-2-2-2-222-2-2-2-2-222-20000000000-2-2-2-222-2-200000000222-2-2-200000020000000000
χ2022-2222222222222-2-2-2-222220022-2-2-2-222-2-2-2-2-22-220000000000-2-2-2-2-2-22200000000-222222000000-20000000000
χ21444144-2144-2-2-2-2-2144-2-2-2-2-20011-2-2-2-2111111004400000000000000-2-21100000000100-200002222000-1-1-1-10000
χ22444144-2144-2-2-2-2-2144-2-2-2-2-20011-2-2-2-2111111004400000000000000-2-21100000000100-20000-2-2-2-200011110000
χ23444144-2144-2-2-2-2-2144-2-2-2-2-20011-2-2-2-211111100-4-40000000000000022-1-100000000-100200002i2i−2i−2i000−i−iii0000
χ24444144-2144-2-2-2-2-2144-2-2-2-2-20011-2-2-2-211111100-4-40000000000000022-1-100000000-10020000−2i−2i2i2i000ii−i−i0000
χ2544441-2441-2411-2-241-2411-2-2001-211-2-21-211-2-2-4-400003-30003-3022-1-10000003-3003-302-100000000000000000000
χ2644441-2441-2411-2-241-2411-2-2001-211-2-21-211-2-2-4-40000-33000-33022-1-1000000-3300-3302-100000000000000000000
χ2744441-2441-2411-2-241-2411-2-2441-211-2-21-211-2-24400-2-2114-2-2114-2-2110000-2-211-2-2110-2100000000000000000000
χ2844441-2441-2411-2-241-2411-2-2-4-41-211-2-21-211-2-2440022-1-1-422-1-1-4-2-211000022-1-122-1-10-2100000000000000000000
χ294444-2144-214-2-2114-214-2-21100-21-2-211-21-2-211-4-4003-30003-3000-1-12200003-3003-3000-1200000000000000000000
χ304444-2144-214-2-2114-214-2-21100-21-2-211-21-2-211-4-400-33000-33000-1-1220000-3300-33000-1200000000000000000000
χ314444-2144-214-2-2114-214-2-21144-21-2-211-21-2-211440011-2-2411-2-2411-2-2000011-2-211-2-201-200000000000000000000
χ324444-2144-214-2-2114-214-2-211-4-4-21-2-211-21-2-2114400-1-122-4-1-122-411-2-20000-1-122-1-12201-200000000000000000000
χ33444-2441-24411111-2441111122-2-21111-2-2-2-2-2-200442222-12222-1000011-2-2-1-1-1-1-1-1-1-1-2001002200000-1-100000000
χ34444-2441-24411111-2441111122-2-21111-2-2-2-2-2-200-4-42222-12222-10000-1-122-1-1-1-1-1-1-1-1200-100-2-2000001100000000
χ35444-2441-24411111-24411111-2-2-2-21111-2-2-2-2-2-20044-2-2-2-21-2-2-2-21000011-2-211111111-200100-2-2000001100000000
χ36444-2441-24411111-24411111-2-2-2-21111-2-2-2-2-2-200-4-4-2-2-2-21-2-2-2-210000-1-12211111111200-1002200000-1-100000000
χ3744-4144-2144-2-2-2-2-2-1-4-42-2-2-2-20011222211-1-1-1-1004-400000000000000-2-2-1-100000000100200002i−2i2i−2i000−ii−ii0000
χ3844-4144-2144-2-2-2-2-2-1-4-42-2-2-2-20011222211-1-1-1-1004-400000000000000-2-2-1-10000000010020000−2i2i−2i2i000i−ii−i0000
χ3944-4144-2144-2-2-2-2-2-1-4-42-2-2-2-20011222211-1-1-1-100-4400000000000000221100000000-100-200002-2-22000-111-10000
χ4044-4144-2144-2-2-2-2-2-1-4-42-2-2-2-20011222211-1-1-1-100-4400000000000000221100000000-100-20000-222-20001-1-110000
χ4144-441-2441-2411-2-2-4-12-411-2-2001-2-1-1221-2-1-122-4400003-3000-33022-1-10000003-300-330-2100000000000000000000
χ4244-441-2441-2411-2-2-4-12-411-2-2001-2-1-1221-2-1-122-440000-330003-3022-1-1000000-33003-30-2100000000000000000000
χ4344-441-2441-2411-2-2-4-12-411-2-24-41-2-1-1221-2-1-1224-400-2-211422-1-1-4-2-2110000-2-21122-1-102-100000000000000000000
χ4444-441-2441-2411-2-2-4-12-411-2-2-441-2-1-1221-2-1-1224-40022-1-1-4-2-2114-2-211000022-1-1-2-21102-100000000000000000000
χ4544-44-2144-214-2-211-42-1-4-2-21100-2122-1-1-2122-1-1-44003-3000-33000-1-12200003-300-330001-200000000000000000000
χ4644-44-2144-214-2-211-42-1-4-2-21100-2122-1-1-2122-1-1-4400-330003-3000-1-1220000-33003-30001-200000000000000000000
χ4744-44-2144-214-2-211-42-1-4-2-2114-4-2122-1-1-2122-1-14-40011-2-24-1-122-411-2-2000011-2-2-1-1220-1200000000000000000000
χ4844-44-2144-214-2-211-42-1-4-2-211-44-2122-1-1-2122-1-14-400-1-122-411-2-2411-2-20000-1-12211-2-20-1200000000000000000000
χ4944-4-2441-244111112-4-4-111112-2-2-2-1-1-1-1-2-22222004-42222-1-2-2-2-2100001122-1-1-1-11111-200-1002-200000-1100000000
χ5044-4-2441-244111112-4-4-111112-2-2-2-1-1-1-1-2-2222200-442222-1-2-2-2-210000-1-1-2-2-1-1-1-11111200100-22000001-100000000
χ5144-4-2441-244111112-4-4-11111-22-2-2-1-1-1-1-2-22222004-4-2-2-2-212222-1000011221111-1-1-1-1-200-100-22000001-100000000
χ5244-4-2441-244111112-4-4-11111-22-2-2-1-1-1-1-2-2222200-44-2-2-2-212222-10000-1-1-2-21111-1-1-1-12001002-200000-1100000000
χ534-404444-4-4-4-444440000-4-4-4-400440000-4-4000000000000000000000000000000000000004-400000000000000000
χ544-404444-4-4-4-444440000-4-4-4-400440000-4-400000000000000000000000000000000000000-4400000000000000000
χ55888-42-42-42-425-4-1-1-42-425-4-1-144-125-4-1-1-12-1-1220000-2-24-2-2-2-24-2-20000000011-2111-2100000000000000000000000
χ56888-42-42-42-425-4-1-1-42-425-4-1-1-4-4-125-4-1-1-12-1-122000022-42222-42200000000-1-12-1-1-12-100000000000000000000000
χ57888-42-42-42-42-45-1-1-42-42-45-1-144-12-45-1-1-12-1-1220000-2-2-24-2-2-2-24-200000000111-2111-200000000000000000000000
χ58888-42-42-42-42-45-1-1-42-42-45-1-1-4-4-12-45-1-1-12-1-1220000222-42222-4200000000-1-1-12-1-1-1200000000000000000000000
χ59888-4-422-4-422-1-15-4-4-422-1-15-4442-1-1-15-42-122-1-100004-2-2-2-24-2-2-2-200000000-2111-211100000000000000000000000
χ60888-4-422-4-422-1-15-4-4-422-1-15-4-4-42-1-1-15-42-122-1-10000-42222-42222000000002-1-1-12-1-1-100000000000000000000000
χ61888-4-422-4-422-1-1-45-4-422-1-1-45442-1-1-1-452-122-1-10000-24-2-2-2-24-2-2-2000000001-2111-21100000000000000000000000
χ62888-4-422-4-422-1-1-45-4-422-1-1-45-4-42-1-1-1-452-122-1-100002-42222-422200000000-12-1-1-12-1-100000000000000000000000
χ6388-8-42-42-42-425-4-1-14-24-25-4-1-14-4-12-5411-1211-2-20000-2-24-2-222-4220000000011-21-1-12-100000000000000000000000
χ6488-8-42-42-42-425-4-1-14-24-25-4-1-1-44-12-5411-1211-2-2000022-422-2-24-2-200000000-1-12-111-2100000000000000000000000
χ6588-8-42-42-42-42-45-1-14-24-2-45-1-14-4-124-511-1211-2-20000-2-2-24-2222-4200000000111-2-1-1-1200000000000000000000000
χ6688-8-42-42-42-42-45-1-14-24-2-45-1-1-44-124-511-1211-2-20000222-42-2-2-24-200000000-1-1-12111-200000000000000000000000
χ6788-8-4-422-4-422-1-15-444-2-2-1-15-44-42-111-542-1-2-21100004-2-2-2-2-4222200000000-21112-1-1-100000000000000000000000
χ6888-8-4-422-4-422-1-15-444-2-2-1-15-4-442-111-542-1-2-2110000-422224-2-2-2-2000000002-1-1-1-211100000000000000000000000
χ6988-8-4-422-4-422-1-1-4544-2-2-1-1-454-42-1114-52-1-2-2110000-24-2-2-22-4222000000001-211-12-1-100000000000000000000000
χ7088-8-4-422-4-422-1-1-4544-2-2-1-1-45-442-1114-52-1-2-21100002-4222-24-2-2-200000000-12-1-11-21100000000000000000000000
χ718-80288-4-2-8-84-4-4-4-40000444400220000-2-20000000000000000000000006-60000000000000000000000000000000
χ728-80288-4-2-8-84-4-4-4-40000444400220000-2-2000000000000000000000000-660000000000000000000000000000000
χ738-8082-48-8-24-822-4-40000-2-244002-40000-24000000000000000000006-600000000000000000000000000000000000
χ748-8082-48-8-24-822-4-40000-2-244002-40000-2400000000000000000000-6600000000000000000000000000000000000
χ758-808-428-84-2-8-4-422000044-2-200-4200004-20000000000000000006-60000000000000000000000000000000000000
χ768-808-428-84-2-8-4-422000044-2-200-4200004-2000000000000000000-660000000000000000000000000000000000000
χ778-80-48824-8-8-222220000-2-2-2-200-4-400004400000000000000000000006-6000000000000000000000000000000000
χ788-80-48824-8-8-222220000-2-2-2-200-4-40000440000000000000000000000-66000000000000000000000000000000000
χ7916161644-8-844-8-8-2-24444-8-8-2-244001-2-2-2441-211-2-200000000000000000000000000000000000000000000000000000
χ801616164-84-84-84-844-2-24-84-844-2-200-2144-2-2-21-2-21100000000000000000000000000000000000000000000000000000
χ811616-1644-8-844-8-8-2-244-4-488-2-244001-222-4-41-2-1-12200000000000000000000000000000000000000000000000000000
χ821616-164-84-84-84-844-2-2-48-4844-2-200-21-4-422-2122-1-100000000000000000000000000000000000000000000000000000
χ8316-16044-8-8-4-488-2-244000022-4-4001-20000-129-90000000000000000000000000000000000000000000000000000000
χ8416-16044-8-8-4-488-2-244000022-4-4001-20000-12-990000000000000000000000000000000000000000000000000000000
χ8516-1604-84-8-48-4844-2-20000-4-42200-2100002-1009-900000000000000000000000000000000000000000000000000000
χ8616-1604-84-8-48-4844-2-20000-4-42200-2100002-100-9900000000000000000000000000000000000000000000000000000
χ8716-160-84-848-48-410-8-2-20000-1082200-2400002-4000000000000000000000000000000000000000000000000000000000
χ8816-160-84-848-48-4-810-2-200008-102200-2400002-4000000000000000000000000000000000000000000000000000000000
χ8916-160-8-84488-4-4-2-210-8000022-108004-20000-42000000000000000000000000000000000000000000000000000000000
χ9016-160-8-84488-4-4-2-2-8100000228-10004-20000-42000000000000000000000000000000000000000000000000000000000

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