Finite Group Databasebeta

← Group #13013766

Character table — Group #13013766

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020202020204040404040808080808080
order124424588881020204102040404040444416162020404080808080808080802488888888888888844881616
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1
χ5111111111111111111111-1-1-1-111111111111111-1-1-1-1iiii−i−i−i−i-1ii−i−ii−ii−i-1-1
χ6111111111111111111111-1-1-1-111111111111111-1-1-1-1−i−i−i−iiiii-1−i−iii−ii−ii-1-1
χ7111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1ii−i−i−ii−ii11
χ8111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1−i−iiii−ii−i11
χ9111111111-1-1111-111-1-1-1-11111i−i-1-111iiii−i−i−i−i-1-11111111111-1-1-1-1-1i−i−iii−i
χ10111111111-1-1111-111-1-1-1-11111i−i-1-111iiii−i−i−i−i-1-111-1-1-1-1-1-1-1-1-11111−iii−ii−i
χ11111111111-1-1111-111-1-1-1-11111−ii-1-111−i−i−i−iiiii-1-11111111111-1-1-1-1-1−iii−i−ii
χ12111111111-1-1111-111-1-1-1-11111−ii-1-111−i−i−i−iiiii-1-111-1-1-1-1-1-1-1-1-11111i−i−ii−ii
χ13111111111-1-1111-111-1-1-1-1-1-1-1-1i−i-1-111iiii−i−i−i−i11-1-1iiii−i−i−i−i1−i−iii-1-111−ii
χ14111111111-1-1111-111-1-1-1-1-1-1-1-1i−i-1-111iiii−i−i−i−i11-1-1−i−i−i−iiiii1ii−i−i11-1-1−ii
χ15111111111-1-1111-111-1-1-1-1-1-1-1-1−ii-1-111−i−i−i−iiiii11-1-1iiii−i−i−i−i1−i−iii11-1-1i−i
χ16111111111-1-1111-111-1-1-1-1-1-1-1-1−ii-1-111−i−i−i−iiiii11-1-1−i−i−i−iiiii1ii−i−i-1-111i−i
χ172222222-2-222222-2222222222200-2-2-2-200000000-2-2-2-20000000020000000000
χ182222222-2-222222-2222222-2-2-2-200-2-2-2-200000000222200000000-20000000000
χ192222222-2-2-2-2222222-2-2-2-222220022-2-20000000022-2-200000000-20000000000
χ202222222-2-2-2-2222222-2-2-2-2-2-2-2-20022-2-200000000-2-2220000000020000000000
χ2122-2-22-22002i−2i2-2-202-22i2i−2i−2i0000000000000000002-22i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i01+i−1−i1−i−1+i000000
χ2222-2-22-22002i−2i2-2-202-22i2i−2i−2i0000000000000000002-22i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0−1−i1+i−1+i1−i000000
χ2322-2-22-22002i−2i2-2-202-22i2i−2i−2i000000000000000000-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0−1+i1−i−1−i1+i000000
χ2422-2-22-22002i−2i2-2-202-22i2i−2i−2i000000000000000000-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i01−i−1+i1+i−1−i000000
χ2522-2-22-2200−2i2i2-2-202-2−2i−2i2i2i0000000000000000002-2−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i01−i−1+i1+i−1−i000000
χ2622-2-22-2200−2i2i2-2-202-2−2i−2i2i2i0000000000000000002-2−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0−1+i1−i−1−i1+i000000
χ2722-2-22-2200−2i2i2-2-202-2−2i−2i2i2i000000000000000000-222i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0−1−i1+i−1+i1−i000000
χ2822-2-22-2200−2i2i2-2-202-2−2i−2i2i2i000000000000000000-222i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i01+i−1−i1−i−1+i000000
χ29444444-14444-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ30444444-14444-1-1-14-1-1-1-1-1-10000-4-4-1-1-1-11111111100000000000000000000000
χ31444444-144-4-4-1-1-1-4-1-1111100004i−4i11-1-1−i−i−i−iiiii00000000000000000000000
χ32444444-144-4-4-1-1-1-4-1-111110000−4i4i11-1-1iiii−i−i−i−i00000000000000000000000
χ33444444-1-4-444-1-1-1-4-1-1-1-1-1-1000000111155−5−555−5−500000000000000000000000
χ34444444-1-4-444-1-1-1-4-1-1-1-1-1-10000001111−5−555−5−55500000000000000000000000
χ35444444-1-4-4-4-4-1-1-14-1-11111000000-1-111i5i5−i5−i5−i5−i5i5i500000000000000000000000
χ36444444-1-4-4-4-4-1-1-14-1-11111000000-1-111−i5−i5i5i5i5i5−i5−i500000000000000000000000
χ374444-4-444i−4i004440-4-40000000000004i−4i0000000000000000000000000000000
χ384444-4-44−4i4i004440-4-4000000000000−4i4i0000000000000000000000000000000
χ394444-4-4-14i−4i00-1-1-10115−55−5000000i5−i5−iiζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ28−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ38ζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ28−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ3800000000000000000000000
χ404444-4-4-14i−4i00-1-1-10115−55−5000000i5−i5−ii−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ28ζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ38−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ28ζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ3800000000000000000000000
χ414444-4-4-14i−4i00-1-1-1011−55−55000000−i5i5−ii−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ38−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ28ζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ38ζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ2800000000000000000000000
χ424444-4-4-14i−4i00-1-1-1011−55−55000000−i5i5−iiζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ38ζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ28−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ38−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ2800000000000000000000000
χ434444-4-4-1−4i4i00-1-1-10115−55−5000000−i5i5i−iζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ28ζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ38ζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ28ζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ3800000000000000000000000
χ444444-4-4-1−4i4i00-1-1-10115−55−5000000−i5i5i−i−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ28−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ38−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ28−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ3800000000000000000000000
χ454444-4-4-1−4i4i00-1-1-1011−55−55000000i5−i5i−i−ζ4+ζ22+ζ36−ζ38ζ4−ζ22−ζ36+ζ38ζ6−ζ12−ζ14+ζ28−ζ6+ζ12+ζ14−ζ28ζ4+ζ22−ζ36−ζ38−ζ4−ζ22+ζ36+ζ38−ζ6−ζ12+ζ14+ζ28ζ6+ζ12−ζ14−ζ2800000000000000000000000
χ464444-4-4-1−4i4i00-1-1-1011−55−55000000i5−i5i−iζ4−ζ22−ζ36+ζ38−ζ4+ζ22+ζ36−ζ38−ζ6+ζ12+ζ14−ζ28ζ6−ζ12−ζ14+ζ28−ζ4−ζ22+ζ36+ζ38ζ4+ζ22−ζ36−ζ38ζ6+ζ12−ζ14−ζ28−ζ6−ζ12+ζ14+ζ2800000000000000000000000
χ4744-4-4-44400004-4-40-4400004i4i−4i−4i0000000000000000000000000000000000000
χ4844-4-4-44400004-4-40-440000−4i−4i4i4i0000000000000000000000000000000000000
χ494-44i−4i0040000-44i−4i00000002+2i−2−2i2−2i−2+2i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000
χ504-44i−4i0040000-44i−4i00000002+2i−2−2i2−2i−2+2i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000
χ514-44i−4i0040000-44i−4i0000000−2−2i2+2i−2+2i2−2i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000
χ524-44i−4i0040000-44i−4i0000000−2−2i2+2i−2+2i2−2i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000
χ534-4−4i4i0040000-4−4i4i00000002−2i−2+2i2+2i−2−2i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000
χ544-4−4i4i0040000-4−4i4i00000002−2i−2+2i2+2i−2−2i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000
χ554-4−4i4i0040000-4−4i4i0000000−2+2i2−2i−2−2i2+2i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000
χ564-4−4i4i0040000-4−4i4i0000000−2+2i2−2i−2−2i2+2i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000
χ5788-8-88-8-2008i−8i-2220-22−2i−2i2i2i00000000000000000000000000000000000000000
χ5888-8-88-8-200−8i8i-2220-222i2i−2i−2i00000000000000000000000000000000000000000
χ5988-8-8-88-20000-22202-22i5−2i5−2i52i500000000000000000000000000000000000000000
χ6088-8-8-88-20000-22202-2−2i52i52i5−2i500000000000000000000000000000000000000000
χ6116-1616i−16i00-400004−4i4i000000000000000000000000000000000000000000000000
χ6216-16−16i16i00-4000044i−4i000000000000000000000000000000000000000000000000

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