Finite Group Databasebeta

← Group #13013765

Character table — Group #13013765

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444444488888881010101016161616161616161616161616162020202020202020202020204040404040808080808080
order124424245881020208101010202020444488404040404040404040404040888888888888488884416161616
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1
χ31111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111111111111-1-1iiii−i−i−i−i-1-1-1ii−i−i-1-1ii−i−i
χ6111111111111111111111-1-1-1-111111111111111-1-1−i−i−i−iiiii-1-1-1−i−iii-1-1−i−iii
χ7111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1ii−i−i11−i−iii
χ8111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1−i−iii11ii−i−i
χ9111111-1-1111111-11-1-11-1-11111i−i11-1-1iiii−i−i−i−i1111111111-1-1-1-1-1-1-1i−ii−ii−i
χ10111111-1-1111111-11-1-11-1-11111i−i11-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-1-1-1-11111i−i−ii−ii
χ11111111-1-1111111-11-1-11-1-11111−ii11-1-1−i−i−i−iiiii1111111111-1-1-1-1-1-1-1−ii−ii−ii
χ12111111-1-1111111-11-1-11-1-11111−ii11-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1-1-11111−iii−ii−i
χ13111111-1-1111111-11-1-11-1-1-1-1-1-1i−i11-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111−i−iii−ii-111-1
χ14111111-1-1111111-11-1-11-1-1-1-1-1-1i−i11-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii111ii−i−i−ii1-1-11
χ15111111-1-1111111-11-1-11-1-1-1-1-1-1−ii11-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i111−i−iiii−i1-1-11
χ16111111-1-1111111-11-1-11-1-1-1-1-1-1−ii11-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111ii−i−ii−i-111-1
χ17222222222-2-2222-2222222222200-2-2-2-200000000-2-200000000-2-220000000000
χ18222222222-2-2222-2222222-2-2-2-200-2-2-2-200000000220000000022-20000000000
χ19222222-2-22-2-222222-2-22-2-2222200-2-22200000000-2-20000000022-20000000000
χ20222222-2-22-2-222222-2-22-2-2-2-2-2-200-2-222000000002200000000-2-220000000000
χ2122-2-22-22-22002-2-20222-2-2-20000000000000000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i01+i−1−i1−i−1+i000000
χ2222-2-22-22-22002-2-20222-2-2-20000000000000000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i0−1−i1+i−1+i1−i000000
χ2322-2-22-22-22002-2-20222-2-2-2000000000000000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i01−i−1+i1+i−1−i000000
χ2422-2-22-22-22002-2-20222-2-2-2000000000000000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i0−1+i1−i−1−i1+i000000
χ2522-2-22-2-222002-2-202-2-2-2220000000000000000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−2i2i0−1−i1+i−1+i1−i000000
χ2622-2-22-2-222002-2-202-2-2-2220000000000000000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2i2i01+i−1−i1−i−1+i000000
χ2722-2-22-2-222002-2-202-2-2-222000000000000000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2i−2i0−1+i1−i−1−i1+i000000
χ2822-2-22-2-222002-2-202-2-2-222000000000000000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2i−2i01−i−1+i1+i−1−i000000
χ2944444444-144-1-1-14-1-1-1-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ3044444444-144-1-1-14-1-1-1-1-1-10000-4-4-1-1-1-11111111100000000000000000000000
χ3144444444-1-4-4-1-1-1-4-1-1-1-1-1-1000000111155−5−555−5−500000000000000000000000
χ3244444444-1-4-4-1-1-1-4-1-1-1-1-1-10000001111−5−555−5−55500000000000000000000000
χ33444444-4-4-144-1-1-1-4-111-11100004i−4i-1-111−i−i−i−iiiii00000000000000000000000
χ34444444-4-4-144-1-1-1-4-111-1110000−4i4i-1-111iiii−i−i−i−i00000000000000000000000
χ35444444-4-4-1-4-4-1-1-14-111-11100000011-1-1i5i5−i5−i5−i5−i5i5i500000000000000000000000
χ36444444-4-4-1-4-4-1-1-14-111-11100000011-1-1−i5−i5i5i5i5i5−i5−i500000000000000000000000
χ374444-4-40044i−4i4440-400-4000000004i−4i000000000000000000000000000000000
χ384444-4-4004−4i4i4440-400-400000000−4i4i000000000000000000000000000000000
χ394444-4-400-14i−4i-1-1-1015−515−5000000−iii5−i5ζ6+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
χ404444-4-400-14i−4i-1-1-1015−515−5000000−iii5−i5−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
χ414444-4-400-14i−4i-1-1-101−551−55000000−ii−i5i5−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
χ424444-4-400-14i−4i-1-1-101−551−55000000−ii−i5i5ζ4+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
χ434444-4-400-1−4i4i-1-1-1015−515−5000000i−i−i5i5ζ6−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
χ444444-4-400-1−4i4i-1-1-1015−515−5000000i−i−i5i5−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
χ454444-4-400-1−4i4i-1-1-101−551−55000000i−ii5−i5−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
χ464444-4-400-1−4i4i-1-1-101−551−55000000i−ii5−i5ζ4−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
χ4744-4-4-44004004-4-40-4004004i4i−4i−4i0000000000000000000000000000000000000
χ4844-4-4-44004004-4-40-400400−4i−4i4i4i0000000000000000000000000000000000000
χ494-44i−4i0000400-44i−4i00000002+2i−2−2i2−2i−2+2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000
χ504-44i−4i0000400-44i−4i00000002+2i−2−2i2−2i−2+2i00000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000
χ514-44i−4i0000400-44i−4i0000000−2−2i2+2i−2+2i2−2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000
χ524-44i−4i0000400-44i−4i0000000−2−2i2+2i−2+2i2−2i00000000000000002ζ7+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+2ζ390000000000000
χ534-4−4i4i0000400-4−4i4i00000002−2i−2+2i2+2i−2−2i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000
χ544-4−4i4i0000400-4−4i4i00000002−2i−2+2i2+2i−2−2i00000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000
χ554-4−4i4i0000400-4−4i4i0000000−2+2i2−2i−2−2i2+2i0000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000
χ564-4−4i4i0000400-4−4i4i0000000−2+2i2−2i−2−2i2+2i00000000000000002ζ13+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+2ζ370000000000000
χ5788-8-88-88-8-200-2220-2-2-222200000000000000000000000000000000000000000
χ5888-8-88-8-88-200-2220-2222-2-200000000000000000000000000000000000000000
χ5988-8-8-8800-200-2220225−25-2−252500000000000000000000000000000000000000000
χ6088-8-8-8800-200-22202−2525-225−2500000000000000000000000000000000000000000
χ6116-1616i−16i0000-4004−4i4i000000000000000000000000000000000000000000000000
χ6216-16−16i16i0000-40044i−4i000000000000000000000000000000000000000000000000

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