Finite Group Databasebeta

← Group #72221558

Character table — Group #72221558

Order 2560.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size112224444444444558888888888101010161616161616161616161616161620202020202032404040404040404040404040646464648080808080808080808080808080160
order1224444588881010102288882020202020202442440404040404040404040404044888824444444488881010102024888816161616161616162
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11
χ3111111111111111111111111111111-1-1111111111111111111-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1
χ4111111111111111111111111111111-1-1111111111111111111-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1
χ511111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111-111111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1
χ611111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111111111-1
χ711111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111111
χ811111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111111-1-1-1-11
χ9111111111111111-1-11111111111-1-1-111111111111111-1-1-1-1-1-11ii−i−iii−i−i-1-1-1-11111-1-1i−ii−iii−i−iii−i−i-1
χ10111111111111111-1-11111111111-1-1-111111111111111-1-1-1-1-1-11−i−iii−i−iii-1-1-1-11111-1-1−ii−ii−i−iii−i−iii-1
χ11111111111111111-1-11111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1ii−i−i−i−iii-1-1-1-1-1-1-1-111i−i−iiii−i−i−i−iii1
χ12111111111111111-1-11111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1−i−iiiii−i−i-1-1-1-1-1-1-1-111−iii−i−i−iiiii−i−i1
χ13111111111111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11111-1-11-1-1i−ii−i−i−iii−i−iii1
χ14111111111111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11111-1-11-1-1−ii−iiii−i−iii−i−i1
χ15111111111111111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i−i−iii1111-111-111i−i−ii−i−iiiii−i−i-1
χ16111111111111111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iiiii−i−i1111-111-111−iii−iii−i−i−i−iii-1
χ1722222222-2-2-2-22222200002222222222-2-2-2-2-20000000022-2-2-2-20000000000000200-22-20000000000000
χ1822222222-2-2-2-2222220000222222222-22-2-2-2-20000000022-2-2-2-20000000000000-2002-220000000000000
χ1922222222-2-2-2-2222-2-20000222222-2-2-22-2-2-2-2-200000000-2-222220000000000000200-2-220000000000000
χ2022222222-2-2-2-2222-2-20000222222-2-2-2-22-2-2-2-200000000-2-222220000000000000-20022-20000000000000
χ2122222-2-2222-2-2222220000-2-2-2-2222220022-2-200000000-2-22-22-2000002222000000000000-2-2000000000
χ2222222-2-2222-2-2222220000-2-2-2-2222220022-2-200000000-2-22-22-200000-2-2-2-200000000000022000000000
χ2322222-2-2222-2-2222-2-20000-2-2-2-222-2-2-20022-2-20000000022-22-22000002i2i−2i−2i000000000000−2i2i000000000
χ2422222-2-2222-2-2222-2-20000-2-2-2-222-2-2-20022-2-20000000022-22-2200000−2i−2i2i2i0000000000002i−2i000000000
χ2522222-2-22-2-222222220000-2-2-2-22222200-2-22200000000-2-2-22-220222200000000000000-2-200000000000
χ2622222-2-22-2-222222220000-2-2-2-22222200-2-22200000000-2-2-22-220-2-2-2-2000000000000002200000000000
χ2722222-2-22-2-222222-2-20000-2-2-2-222-2-2-200-2-22200000000222-22-202i2i−2i−2i00000000000000−2i2i00000000000
χ2822222-2-22-2-222222-2-20000-2-2-2-222-2-2-200-2-22200000000222-22-20−2i−2i2i2i000000000000002i−2i00000000000
χ2922-22-2002002-2-2-222222−2−200002-2-22-200002-22222−2−2−2−2000-20202-22-2000022−2−200000000002−22−200000
χ3022-22-2002002-2-2-222222−2−200002-2-22-200002-22222−2−2−2−2000-2020-22-22000022−2−20000000000−22−2200000
χ3122-22-2002002-2-2-2222−2−22200002-2-22-200002-2−2−2−2−22222000-20202-22-20000−2−2220000000000−22−2200000
χ3222-22-2002002-2-2-2222−2−22200002-2-22-200002-2−2−2−2−22222000-2020-22-220000−2−22200000000002−22−200000
χ3322-22-2002002-2-2-22-2-222−2−200002-22-2200002-22222−2−2−2−200020-202i−2i−2i2i0000−2−2220000000000i2−i2−i2i200000
χ3422-22-2002002-2-2-22-2-222−2−200002-22-2200002-22222−2−2−2−200020-20−2i2i2i−2i0000−2−2220000000000−i2i2i2−i200000
χ3522-22-2002002-2-2-22-2-2−2−22200002-22-2200002-2−2−2−2−2222200020-202i−2i−2i2i000022−2−20000000000−i2i2i2−i200000
χ3622-22-2002002-2-2-22-2-2−2−22200002-22-2200002-2−2−2−2−2222200020-20−2i2i2i−2i000022−2−20000000000i2−i2−i2i200000
χ3722-2-220022-200-2-22222−22−20000-22-2-22002-20022−2−222−2−200-2020000002-22-22−22−2000000000000002−22−20
χ3822-2-220022-200-2-22222−22−20000-22-2-22002-20022−2−222−2−200-202000000-22-222−22−200000000000000−22−220
χ3922-2-220022-200-2-2222−22−220000-22-2-22002-200−2−222−2−22200-2020000002-22-2−22−2200000000000000−22−220
χ4022-2-220022-200-2-2222−22−220000-22-2-22002-200−2−222−2−22200-202000000-22-22−22−22000000000000002−22−20
χ4122-2-220022-200-2-22-2-22−22−20000-2222-2002-20022−2−222−2−20020-20000002i−2i−2i2i−22−2200000000000000i2−i2−i2i20
χ4222-2-220022-200-2-22-2-22−22−20000-2222-2002-20022−2−222−2−20020-2000000−2i2i2i−2i−22−2200000000000000−i2i2i2−i20
χ4322-2-220022-200-2-22-2-2−22−220000-2222-2002-200−2−222−2−2220020-20000002i−2i−2i2i2−22−200000000000000−i2i2i2−i20
χ4422-2-220022-200-2-22-2-2−22−220000-2222-2002-200−2−222−2−2220020-2000000−2i2i2i−2i2−22−200000000000000i2−i2−i2i20
χ454444444-14444-1-1-1004444-1-1-1-1-1-100044-1-1-1-1-1-1-1-1-1-1-1-10000004000000000000-1-1-1-1000000000000000
χ464444444-14444-1-1-1004444-1-1-1-1-1-1000-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000-40000000000001111000000000000000
χ474444444-14444-1-1-100-4-4-4-4-1-1-1-1-1-100044-1-1-1-111111111000000-4000000000000-111-1000000000000000
χ484444444-14444-1-1-100-4-4-4-4-1-1-1-1-1-1000-4-4-1-1-1-11111111100000040000000000001-1-11000000000000000
χ494444444-1-4-4-4-4-1-1-1000000-1-1-1-1-1-10004-411115−55−55−55−50000000000000000000-15−51000000000000000
χ504444444-1-4-4-4-4-1-1-1000000-1-1-1-1-1-10004-41111−55−55−55−550000000000000000000-1−551000000000000000
χ514444444-1-4-4-4-4-1-1-1000000-1-1-1-1-1-1000-4411115−55−55−55−500000000000000000001−55-1000000000000000
χ524444444-1-4-4-4-4-1-1-1000000-1-1-1-1-1-1000-441111−55−55−55−55000000000000000000015−5-1000000000000000
χ53444-4-40040000444442-2-220000-4-44-4-400000022-2-2-2-2220000000000000002-2-220000000000000000000
χ54444-4-4004000044444-222-20000-4-44-4-4000000-2-22222-2-2000000000000000-222-20000000000000000000
χ55444-4-40040000444-4-42-2-220000-4-4-44400000022-2-2-2-222000000000000000-222-20000000000000000000
χ56444-4-40040000444-4-4-222-20000-4-4-444000000-2-22222-2-20000000000000002-2-220000000000000000000
χ5744-44-400400-44-4-4444000000004-4-44-40000-440000000000040-400000000000000000000000000000000
χ5844-44-400400-44-4-44-4-4000000004-44-440000-4400000000000-40400000000000000000000000000000000
χ5944-4-44004-4400-4-444400000000-44-4-4400-4400000000000040-4000000000000000000000000000000000
χ6044-4-44004-4400-4-44-4-400000000-4444-400-44000000000000-404000000000000000000000000000000000
χ6188888-8-8-288-8-8-2-2-20000002222-2-200000-2-2220000000000000000000000000000000000000000000000
χ6288888-8-8-2-8-888-2-2-20000002222-2-20000022-2-20000000000000000000000000000000000000000000000
χ63888-8-800-20000-2-2-2004-4-442525−25−2522000000000−1+5−1−51−51+51−51+5−1+5−1−500000000000000000000000000000000000000
χ64888-8-800-20000-2-2-2004-4-44−25−25252522000000000−1−5−1+51+51−51+51−5−1−5−1+500000000000000000000000000000000000000
χ65888-8-800-20000-2-2-200-444-42525−25−25220000000001−51+5−1+5−1−5−1+5−1−51−51+500000000000000000000000000000000000000
χ66888-8-800-20000-2-2-200-444-4−25−252525220000000001+51−5−1−5−1+5−1−5−1+51+51−500000000000000000000000000000000000000
χ6788-88-800-2008-822-2004242−42−420000-220000000-22−2−2−2−2222200000000000000000000000000000000000000
χ6888-88-800-2008-822-200−42−4242420000-220000000-222222−2−2−2−200000000000000000000000000000000000000
χ6988-88-800-200-8822-20000000000-2200000002-210−1010−10−1010−101000000000000000000000000000000000000000
χ7088-88-800-200-8822-20000000000-2200000002-2−1010−101010−1010−1000000000000000000000000000000000000000
χ7188-8-8800-28-80022-20042−4242−4200002-200000-2200−2−222−2−22200000000000000000000000000000000000000
χ7288-8-8800-28-80022-200−4242−424200002-200000-220022−2−222−2−200000000000000000000000000000000000000
χ7388-8-8800-2-880022-200000000002-2000002-20010−10−101010−10−101000000000000000000000000000000000000000
χ7488-8-8800-2-880022-200000000002-2000002-200−101010−10−101010−1000000000000000000000000000000000000000
χ758-80004-48000000-88-800004-44-400000000000000000004-4000000000000000000000000000000000000
χ768-80004-48000000-8-8800004-44-40000000000000000000-44000000000000000000000000000000000000
χ778-8000-448000000-88-80000-44-440000000000000000000-44000000000000000000000000000000000000
χ788-8000-448000000-8-880000-44-4400000000000000000004-4000000000000000000000000000000000000
χ7916-160008-8-4000045−454000000−2+252−25−2−252+25000000000000000000000000000000000000000000000000000000000
χ8016-160008-8-40000−45454000000−2−252+25−2+252−25000000000000000000000000000000000000000000000000000000000
χ8116-16000-88-4000045−4540000002−25−2+252+25−2−25000000000000000000000000000000000000000000000000000000000
χ8216-16000-88-40000−454540000002+25−2−252−25−2+25000000000000000000000000000000000000000000000000000000000

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