Finite Group Databasebeta

← Group #13026458

Character table — Group #13026458

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222224444444444445588888888888888881010101010101016161616161616162020202040404040404040404040404080808080
order1224488884458810202040404040222488102020202020404040404040244888810102020404040404488248816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-11111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111111111111111-1-11111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ91111111-1-1-1-111-1111-1-1-1-11111-1-11-1-1-1-11-1-11111111-1-1111111-1-1-1-1-1-11-111-1-111-1-111-1-11-11-1
χ101111111-1-1-1-111-1111-1-1-1-11111-1-11-1-1-1-11-1-11111111-1-1111111-1-1-1-1-1-11-111-1-1-1-111-1-111-11-11
χ111111111-1-1-1-111-1111-1-1-1-111-1-1111-1-1-1-11-1-11111111-1-111-1-1-1-11111-1-11-1-1-11111-1-111-1-1-11-11
χ121111111-1-1-1-111-1111-1-1-1-111-1-1111-1-1-1-11-1-11111111-1-111-1-1-1-11111-1-11-1-1-111-1-111-1-1111-11-1
χ131111111-1-1-1-111-1111-1-1-1-1-1-111-1-11-1-1-1-11-1-11111-1-1-111-1-11111-1-1-1-111-11-1-111ii−i−i−i−iiii−i−ii
χ141111111-1-1-1-111-1111-1-1-1-1-1-111-1-11-1-1-1-11-1-11111-1-1-111-1-11111-1-1-1-111-11-1-111−i−iiiii−i−i−iii−i
χ151111111-1-1-1-111-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-111-1-1-1-1-1-1111111-1111-1-1ii−i−i−i−iii−iii−i
χ161111111-1-1-1-111-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-111-1-1-1-1-1-1111111-1111-1-1−i−iiiii−i−ii−i−ii
χ1722222-2-222-2-22-2222222222200002-2-2-2-2222-2-2-2-222222-2-200000000-2-2-220000000000000000
χ1822222-2-222-2-22-222222222-2-200002-2-2-2-2222-2-2-2-2-2-2-2-2-22200000000222-20000000000000000
χ1922222-2-2-2-2222-2-2222-2-2-2-2220000222222-2-2-2-2-2-2222-2-2-2-20000000022-2-20000000000000000
χ2022222-2-2-2-2222-2-2222-2-2-2-2-2-20000222222-2-2-2-2-2-2-2-2-2222200000000-2-2220000000000000000
χ2122-22-22200002-202-2-20000222-200-2000020022-2-2-22-2002222-2-2000000-202-200000000000000
χ2222-22-22200002-202-2-2000022-2200-2000020022-2-2-22-20022-2-222000000-20-2200000000000000
χ2322-22-22200002-202-2-20000-2-22-200-2000020022-2-22-2200-2-222-2-200000020-2200000000000000
χ2422-22-22200002-202-2-20000-2-2-2200-2000020022-2-22-2200-2-2-2-222000000202-200000000000000
χ2522-22-2-2-200002202-2-2000022002i−2i-20000200-2-222-22-200-2-200002i2i−2i−2i0020002i−2i000000000000
χ2622-22-2-2-200002202-2-200002200−2i2i-20000200-2-222-22-200-2-20000−2i−2i2i2i002000−2i2i000000000000
χ2722-22-2-2-200002202-2-20000-2-2002i−2i-20000200-2-2222-22002200002i2i−2i−2i00-2000−2i2i000000000000
χ2822-22-2-2-200002202-2-20000-2-200−2i2i-20000200-2-2222-2200220000−2i−2i2i2i00-20002i−2i000000000000
χ2922-2-2200220020-22222222220000-20000-2-2-20000-2-22220000000000000-200002−22−22−22−20000
χ3022-2-2200220020-22222222220000-20000-2-2-20000-2-22220000000000000-20000−22−22−22−220000
χ3122-2-2200220020-22222222-2-20000-20000-2-2-2000022-2-2-2000000000000020000i2−i2i2−i2−i2i2−i2i20000
χ3222-2-2200220020-22222222-2-20000-20000-2-2-2000022-2-2-2000000000000020000−i2i2−i2i2i2−i2i2−i20000
χ3322-2-2200-2-200202222-2-2-2-2220000-20000-2220000-2-22-2-20000000000000200002−2−222−2−220000
χ3422-2-2200-2-200202222-2-2-2-2220000-20000-2220000-2-22-2-2000000000000020000−222−2−222−20000
χ3522-2-2200-2-200202222-2-2-2-2-2-20000-20000-222000022-2220000000000000-20000i2−i2−i2i2−i2i2i2−i20000
χ3622-2-2200-2-200202222-2-2-2-2-2-20000-20000-222000022-2220000000000000-20000−i2i2i2−i2i2−i2−i2i20000
χ3744444444444-144-1-1-1-1-1-1-1004444-1-1-1-1-1-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-100000000000000000000
χ3844444444444-144-1-1-1-1-1-1-100-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000001111111100000000000000000000
χ394444444-4-4-4-4-14-4-1-1-111110044-4-4-11111-111-1-1-1-10000000-1-1-1-1111100000000000000000000
χ404444444-4-4-4-4-14-4-1-1-1111100-4-444-11111-111-1-1-1-100000001111-1-1-1-100000000000000000000
χ4144444-4-444-4-4-1-44-1-1-1-1-1-1-1000000-11111-1-1-1111100000005−55−55−55−500000000000000000000
χ4244444-4-444-4-4-1-44-1-1-1-1-1-1-1000000-11111-1-1-111110000000−55−55−55−5500000000000000000000
χ4344444-4-4-4-444-1-4-4-1-1-11111000000-1-1-1-1-1-111111100000005−55−5−55−5500000000000000000000
χ4444444-4-4-4-444-1-4-4-1-1-11111000000-1-1-1-1-1-11111110000000−55−555−55−500000000000000000000
χ45444-4-40000004004-4-4000044000040000-40000004-4-400000000000000000000000000000000
χ46444-4-40000004004-4-40000-4-4000040000-4000000-44400000000000000000000000000000000
χ4744-44-4440000-1-40-111i5i5−i5−i5004-4001i5i5−i5−i5-1i5−i5-1-1110000000-1-111i5−i5−i5i500000000000000000000
χ4844-44-4440000-1-40-111i5i5−i5−i500-44001i5i5−i5−i5-1i5−i5-1-111000000011-1-1−i5i5i5−i500000000000000000000
χ4944-44-4440000-1-40-111−i5−i5i5i5004-4001−i5−i5i5i5-1−i5i5-1-1110000000-1-111−i5i5i5−i500000000000000000000
χ5044-44-4440000-1-40-111−i5−i5i5i500-44001−i5−i5i5i5-1−i5i5-1-111000000011-1-1i5−i5−i5i500000000000000000000
χ5144-44-4-4-40000-140-111i5i5−i5−i500004i−4i1−i5−i5i5i5-1i5−i511-1-100000005−5−55−i−iii00000000000000000000
χ5244-44-4-4-40000-140-111i5i5−i5−i50000−4i4i1−i5−i5i5i5-1i5−i511-1-10000000−555−5ii−i−i00000000000000000000
χ5344-44-4-4-40000-140-111−i5−i5i5i500004i−4i1i5i5−i5−i5-1−i5i511-1-10000000−555−5−i−iii00000000000000000000
χ5444-44-4-4-40000-140-111−i5−i5i5i50000−4i4i1i5i5−i5−i5-1−i5i511-1-100000005−5−55ii−i−i00000000000000000000
χ554-400022−222i2−2i22i−2i400-4002i2−2i22i2−2i24-4000002i−2i2i−2i00022−22000002i2−2i222−22000000002i−2i000000000000000000
χ564-400022−222i2−2i22i−2i400-4002i2−2i22i2−2i2-44000002i−2i2i−2i00022−2200000−2i22i2−222200000000−2i2i000000000000000000
χ574-400022−22−2i22i2−2i2i400-400−2i22i2−2i22i24-400000−2i2i−2i2i00022−2200000−2i22i222−2200000000−2i2i000000000000000000
χ584-400022−22−2i22i2−2i2i400-400−2i22i2−2i22i2-4400000−2i2i−2i2i00022−22000002i2−2i2−2222000000002i−2i000000000000000000
χ594-4000−22222i2−2i2−2i2i400-4002i2−2i22i2−2i24-400000−2i2i−2i2i000−2222000002i2−2i2−222200000000−2i2i000000000000000000
χ604-4000−22222i2−2i2−2i2i400-4002i2−2i22i2−2i2-4400000−2i2i−2i2i000−222200000−2i22i222−22000000002i−2i000000000000000000
χ614-4000−2222−2i22i22i−2i400-400−2i22i2−2i22i24-4000002i−2i2i−2i000−222200000−2i22i2−2222000000002i−2i000000000000000000
χ624-4000−2222−2i22i22i−2i400-400−2i22i2−2i22i2-44000002i−2i2i−2i000−2222000002i2−2i222−2200000000−2i2i000000000000000000
χ63888-8-8000000-200-2222i52i5−2i5−2i5000000-200002−2i52i5000000000000000000000000000000000000000
χ64888-8-8000000-200-222−2i5−2i52i52i5000000-2000022i5−2i5000000000000000000000000000000000000000
χ6588-8-88008800-20-8-2-2-2-2-2-2-200000020000222000000000000000000000000000000000000000
χ6688-8-8800-8-800-208-2-2-22222000000200002-2-2000000000000000000000000000000000000000
χ678-800042−424i2−4i24i−4i-20022i5−2i52ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ390000000−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38000−22i10−i1000000000000000000000000000000000000
χ688-800042−424i2−4i24i−4i-2002−2i52i52ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ290000000ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38000−22−i10i1000000000000000000000000000000000000
χ698-800042−42−4i24i2−4i4i-20022i5−2i5−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ390000000ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38000−22i10−i1000000000000000000000000000000000000
χ708-800042−42−4i24i2−4i4i-2002−2i52i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ290000000−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38000−22−i10i1000000000000000000000000000000000000
χ718-8000−42424i2−4i2−4i4i-20022i5−2i52ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ292ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ390000000ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ380002−2−i10i1000000000000000000000000000000000000
χ728-8000−42424i2−4i2−4i4i-2002−2i52i52ζ13+2ζ31+2ζ37+2ζ39−2ζ13−2ζ31−2ζ37−2ζ392ζ7+2ζ21+2ζ23+2ζ29−2ζ7−2ζ21−2ζ23−2ζ290000000−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ380002−2i10−i1000000000000000000000000000000000000
χ738-8000−4242−4i24i24i−4i-20022i5−2i5−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ29−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ390000000−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ380002−2−i10i1000000000000000000000000000000000000
χ748-8000−4242−4i24i24i−4i-2002−2i52i5−2ζ13−2ζ31−2ζ37−2ζ392ζ13+2ζ31+2ζ37+2ζ39−2ζ7−2ζ21−2ζ23−2ζ292ζ7+2ζ21+2ζ23+2ζ290000000ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ380002−2i10−i1000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.